diff --git a/.gitignore b/.gitignore
index 0730d1d0d..f79db28bc 100644
--- a/.gitignore
+++ b/.gitignore
@@ -182,3 +182,8 @@ node_modules/
 wheelhouse/
 
 pytest.ini
+
+# Artifacts written to the repo root by some tests/examples
+/res
+/results/
+/schedule_*.pkl
diff --git a/docs/AnalogInfo.md b/docs/AnalogInfo.md
index e57f27ce0..75b7142b7 100644
--- a/docs/AnalogInfo.md
+++ b/docs/AnalogInfo.md
@@ -19,14 +19,14 @@ The {code}`results` directory contains the results used in the paper {cite:label
 
 ## Codes
 
-The {code}`codes` directory contains the parity-check matrices of the codes used in the paper {cite:labelpar}`berent2023analog`.
+The parity-check matrices of the codes used in the paper {cite:labelpar}`berent2023analog` can be found in the directory {code}`src/mqt/qecc/codes/instances/lifted_product`.
 Three dimensional toric codes can either be constructed with the hypergraph product construction
 or with a library, e.g., panqec {cite:labelpar}`huang2023panceq`.
 
 ## Code construction
 
 The {code}`code_construction` directory contains the code used to construct higher-dimensional hypergraph
-product codes and used the {code}`compute_distances.sh` script to automatically compute bounds on the
+product codes, utilizing the generator {code}`src/mqt/qecc/codes/constructions/hypergraph_product_code.py`, and used the {code}`compute_distances.sh` script to automatically compute bounds on the
 distances of the constructed codes using the GAP library QDistRnd {cite:labelpar}`pryadko2023qdistrnd`.
 
 ## Utils
diff --git a/docs/ExactSynthesis.md b/docs/ExactSynthesis.md
index add5264b4..93e415a62 100644
--- a/docs/ExactSynthesis.md
+++ b/docs/ExactSynthesis.md
@@ -34,7 +34,7 @@ Let us synthesize an encoder for the $[[4,2,2]]$ iceberg code — a small CSS co
 
 ```{code-cell} ipython3
 from mqt.qecc.codes import construct_iceberg_code
-from mqt.qecc.codes.pauli import CheckMatrix
+from mqt.qecc.codes.core.pauli import CheckMatrix
 
 code = construct_iceberg_code(2)  # [[4,2,2]] iceberg code
 print(f"[[{code.n},{code.k},{code.distance}]] iceberg code")
@@ -97,7 +97,7 @@ For non-CSS stabilizer codes, encoding circuits are built from the full Clifford
 The gate set for non-CSS synthesis defaults to $\{H, S, \text{CX}\}$ (standard Clifford). The extended gate set $\{H, S, \sqrt{X}, \text{CX}, \text{CZ}\}$ can find shorter circuits:
 
 ```{code-cell} ipython3
-from mqt.qecc.codes.pauli import StabilizerTableau
+from mqt.qecc.codes.core.pauli import StabilizerTableau
 from mqt.qecc.circuit_synthesis.exact import get_clifford_extended_gate_set
 
 stabs = ["XZZXI", "IXZZX", "XIXZZ", "ZXIXZ"]
diff --git a/examples/add_new_gate_example.py b/examples/add_new_gate_example.py
index 71cb27148..6d00234df 100644
--- a/examples/add_new_gate_example.py
+++ b/examples/add_new_gate_example.py
@@ -29,7 +29,7 @@
     SymbolicGateOperation,
     get_standard_clifford_gate_set,
 )
-from mqt.qecc.codes.pauli import StabilizerTableau
+from mqt.qecc.codes.core.pauli import StabilizerTableau
 
 if TYPE_CHECKING:
     import numpy as np
diff --git a/scripts/encoding_circuits/codes/css/108_8_10.txt b/scripts/encoding_circuits/codes/css/108_8_10.txt
deleted file mode 100644
index cd353ca6d..000000000
--- a/scripts/encoding_circuits/codes/css/108_8_10.txt
+++ /dev/null
@@ -1,109 +0,0 @@
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diff --git a/scripts/examples/atd_example.py b/scripts/examples/atd_example.py
index decf6e694..d506763d6 100644
--- a/scripts/examples/atd_example.py
+++ b/scripts/examples/atd_example.py
@@ -16,16 +16,16 @@
 from mqt.qecc.analog_information_decoding.simulators.analog_tannergraph_decoding import AtdSimulator
 from mqt.qecc.analog_information_decoding.utils.data_utils import BpParams
 
-code_path = "src/mqt/qecc/analog_information_decoding/codes/lifted_product/lp_l="
+code_path = "src/mqt/qecc/codes/instances/lifted_product/lp_l="
 s = np.linspace(0.10, 0.4, 11)
 p = 0.05
 for bp_method in ["msl"]:
     for decoder in ["atd"]:
         for c in [16, 21, 30]:
-            Hx = scipy.sparse.load_npz(code_path + str(c) + "_hx.txt").toarray()
-            Hz = scipy.sparse.load_npz(code_path + str(c) + "_hz.txt").toarray()
-            Lx = scipy.sparse.load_npz(code_path + str(c) + "_lx.txt").toarray()
-            Lz = scipy.sparse.load_npz(code_path + str(c) + "_lz.txt").toarray()
+            Hx = scipy.sparse.load_npz(code_path + str(c) + "_hx.npz").toarray()
+            Hz = scipy.sparse.load_npz(code_path + str(c) + "_hz.npz").toarray()
+            Lx = scipy.sparse.load_npz(code_path + str(c) + "_lx.npz").toarray()
+            Lz = scipy.sparse.load_npz(code_path + str(c) + "_lz.npz").toarray()
             lers = []
             ebs = []
             for sigma in s:
diff --git a/scripts/ft_stateprep/eval/estimate_logical_error_rate.py b/scripts/ft_stateprep/eval/estimate_logical_error_rate.py
index 1f057b610..1654a7406 100644
--- a/scripts/ft_stateprep/eval/estimate_logical_error_rate.py
+++ b/scripts/ft_stateprep/eval/estimate_logical_error_rate.py
@@ -23,7 +23,12 @@
     heuristic_verification_circuit,
     naive_verification_circuit,
 )
-from mqt.qecc.codes import HexagonalColorCode, SquareOctagonColorCode
+from mqt.qecc.codes import (
+    HexagonalColorCode,
+    RotatedSurfaceCode,
+    SquareOctagonColorCode,
+    construct_quantum_hamming_code,
+)
 
 
 def main() -> None:
@@ -57,7 +62,7 @@ def main() -> None:
     code_name = args.code
     if "surface" in code_name:
         d = args.distance
-        code = CSSCode.from_code_name("surface", d)
+        code = RotatedSurfaceCode(d)
         code_name = f"rotated_surface_d{d}"
     elif "cc_4_8_8" in code_name:
         d = 5
@@ -65,6 +70,10 @@ def main() -> None:
     elif "cc_6_6_6" in code_name:
         d = 5
         code = HexagonalColorCode(d)
+    elif "hamming" in code_name:
+        # The [[15, 7, 3]] quantum Hamming code (previously a hard-coded instance,
+        # now generated) since it was removed from CSSCode.from_code_name.
+        code = construct_quantum_hamming_code(4)
     elif code_name in available_codes:
         code = CSSCode.from_code_name(code_name)
     else:
diff --git a/src/mqt/qecc/analog_information_decoding/code_construction/code_constructor.py b/src/mqt/qecc/analog_information_decoding/code_construction/code_constructor.py
index 2882df0ab..b2888f65f 100644
--- a/src/mqt/qecc/analog_information_decoding/code_construction/code_constructor.py
+++ b/src/mqt/qecc/analog_information_decoding/code_construction/code_constructor.py
@@ -17,101 +17,17 @@
 import ldpc.codes
 import numpy as np
 import scipy.io as sio
-import scipy.sparse as scs
 from bposd.hgp import hgp
 from scipy import sparse
 
 from mqt.qecc import mod2
 
+from ...codes.constructions.hypergraph_product_code import generate_3d_product_code, generate_4d_product_code
+
 if TYPE_CHECKING:
     from numpy.typing import NDArray
 
 
-def is_all_zeros(array: NDArray[np.int32]) -> bool:
-    """Check if array is all zeros."""
-    return not np.any(array)
-
-
-def run_checks_scipy(
-    d_1: NDArray[np.int32], d_2: NDArray[np.int32], d_3: NDArray[np.int32], d_4: NDArray[np.int32]
-) -> None:
-    """Run checks on the boundary maps."""
-    sd_1 = scs.csr_matrix(d_1)
-    sd_2 = scs.csr_matrix(d_2)
-    sd_3 = scs.csr_matrix(d_3)
-    sd_4 = scs.csr_matrix(d_4)
-
-    if not (
-        is_all_zeros((sd_1 * sd_2).todense() % 2)
-        and is_all_zeros((sd_2 * sd_3).todense() % 2)
-        and is_all_zeros((sd_3 * sd_4).todense() % 2)
-    ):
-        msg = "Error generating 4D code, boundary maps do not square to zero"
-        raise RuntimeError(msg)
-
-
-def generate_4d_product_code(
-    a_1: NDArray[np.int32], a_2: NDArray[np.int32], a_3: NDArray[np.int32], p: NDArray[np.int32], checks: bool = True
-) -> tuple[NDArray[np.int32], NDArray[np.int32], NDArray[np.int32], NDArray[np.int32]]:
-    """Generate 4D product code."""
-    r, c = p.shape
-    id_r: NDArray[np.int32] = np.identity(r, dtype=np.int32)
-    id_c: NDArray[np.int32] = np.identity(c, dtype=np.int32)
-    id_n0: NDArray[np.int32] = np.identity(a_1.shape[0], dtype=np.int32)
-    id_n1: NDArray[np.int32] = np.identity(a_2.shape[0], dtype=np.int32)
-    id_n2: NDArray[np.int32] = np.identity(a_3.shape[0], dtype=np.int32)
-    id_n3: NDArray[np.int32] = np.identity(a_3.shape[1], dtype=np.int32)
-
-    d_1: NDArray[np.int32] = np.hstack((np.kron(a_1, id_r), np.kron(id_n0, p))).astype(np.int32)
-
-    x = np.hstack((np.kron(a_2, id_r), np.kron(id_n1, p)))
-    y = np.kron(a_1, id_c)
-    dims = (y.shape[0], x.shape[1] - y.shape[1])
-    z = np.hstack((np.zeros(dims, dtype=np.int32), y))
-    d_2 = np.vstack((x, z))
-
-    x = np.hstack((np.kron(a_3, id_r), np.kron(id_n2, p)))
-    y = np.kron(a_2, id_c)
-    dims = (y.shape[0], x.shape[1] - y.shape[1])
-    z = np.hstack((np.zeros(dims, dtype=np.int32), y))
-    d_3: NDArray[np.int32] = np.vstack((x, z)).astype(np.int32)
-
-    d_4: NDArray[np.int32] = np.vstack((np.kron(id_n3, p), np.kron(a_3, id_c)))
-
-    if checks:
-        run_checks_scipy(d_1, d_2, d_3, d_4)
-
-    return d_1, d_2, d_3, d_4
-
-
-def generate_3d_product_code(
-    a_1: NDArray[np.int32], a_2: NDArray[np.int32], p: NDArray[np.int32]
-) -> tuple[NDArray[np.int32], NDArray[np.int32], NDArray[np.int32]]:
-    """Generate 3D product code."""
-    r, c = p.shape
-    id_r: NDArray[np.int32] = np.identity(r, dtype=np.int32)
-    id_c: NDArray[np.int32] = np.identity(c, dtype=np.int32)
-    id_n0: NDArray[np.int32] = np.identity(a_1.shape[0], dtype=np.int32)
-    id_n1: NDArray[np.int32] = np.identity(a_2.shape[0], dtype=np.int32)
-    id_n2: NDArray[np.int32] = np.identity(a_2.shape[1], dtype=np.int32)
-
-    d_1: NDArray[np.int32] = np.hstack((np.kron(a_1, id_r), np.kron(id_n0, p)))
-
-    x = np.hstack((np.kron(a_2, id_r), np.kron(id_n1, p)))
-    y = np.kron(a_1, id_c)
-    dims = (y.shape[0], x.shape[1] - y.shape[1])
-    z = np.hstack((np.zeros(dims, dtype=np.int32), y))
-    d_2: NDArray[np.int32] = np.vstack((x, z))
-
-    d_3: NDArray[np.int32] = np.vstack((np.kron(id_n2, p), np.kron(a_2, id_c)))
-
-    if not (is_all_zeros(d_1 @ d_2 % 2) and is_all_zeros(d_2 @ d_3 % 2)):
-        msg = "Error generating 3D code, boundary maps do not square to zero"
-        raise RuntimeError(msg)
-
-    return d_1, d_2, d_3
-
-
 def create_outpath(codename: str) -> str:
     """Create output path for code files."""
     path = f"generated_codes/{codename}/"
diff --git a/src/mqt/qecc/analog_information_decoding/code_construction/sparse_code_constructor.py b/src/mqt/qecc/analog_information_decoding/code_construction/sparse_code_constructor.py
index 80f2c1546..6940905b0 100644
--- a/src/mqt/qecc/analog_information_decoding/code_construction/sparse_code_constructor.py
+++ b/src/mqt/qecc/analog_information_decoding/code_construction/sparse_code_constructor.py
@@ -22,100 +22,13 @@
 
 from mqt.qecc.mod2 import rank
 
+from ...codes.constructions.hypergraph_product_code import generate_sparse_3d_product_code
 from . import code_constructor
 
 if TYPE_CHECKING:
     from numpy.typing import NDArray
 
 
-def is_all_zeros(array: NDArray[np.int_]) -> bool:
-    """Check if array is all zeros."""
-    return not np.any(array)
-
-
-def sparse_all_zeros(mat: csr_matrix) -> bool:
-    """Check if sparse matrix is all zeros."""
-    mat.data %= 2
-    return bool(mat.sum() == 0)
-
-
-def run_checks_scipy(d_1: csr_matrix, d_2: csr_matrix, d_3: csr_matrix, d_4: csr_matrix) -> None:
-    """Run checks on the boundary maps."""
-    if not (sparse_all_zeros(d_1 @ d_2) and sparse_all_zeros(d_2 @ d_3) and sparse_all_zeros(d_3 @ d_4)):
-        msg = "Error generating 4D code, boundary maps do not square to zero"
-        raise RuntimeError(msg)
-
-
-def generate_4d_product_code(
-    a_1: csr_matrix,
-    a_2: csr_matrix,
-    a_3: csr_matrix,
-    p: csr_matrix,
-    checks: bool = True,
-) -> tuple[csr_matrix, csr_matrix, csr_matrix, csr_matrix]:
-    """Generate 4D HGP code."""
-    r, c = p.shape
-
-    id_r = sparse.identity(r, dtype=int)
-    id_c = sparse.identity(c, dtype=int)
-    id_n0 = sparse.identity(a_1.shape[0], dtype=int)
-    id_n1 = sparse.identity(a_2.shape[0], dtype=int)
-    id_n2 = sparse.identity(a_3.shape[0], dtype=int)
-    id_n3 = sparse.identity(a_3.shape[1], dtype=int)
-
-    d_1 = sparse.hstack((sparse.kron(a_1, id_r), sparse.kron(id_n0, p)))
-
-    x = sparse.hstack((sparse.kron(a_2, id_r), sparse.kron(id_n1, p)))
-    y = sparse.kron(a_1, id_c)
-    dims = (y.shape[0], x.shape[1] - y.shape[1])
-    nmat = csr_matrix(np.zeros(dims))
-    z = sparse.hstack((nmat, y))
-    d_2 = sparse.vstack((x, z))
-
-    x = sparse.hstack((sparse.kron(a_3, id_r), sparse.kron(id_n2, p)))
-    y = sparse.kron(a_2, id_c)
-    dims = (y.shape[0], x.shape[1] - y.shape[1])
-    mat = csr_matrix(np.zeros(dims))
-    z = sparse.hstack([mat, y])
-    d_3 = sparse.vstack((x, z))
-
-    d_4 = sparse.vstack((sparse.kron(id_n3, p), sparse.kron(a_3, id_c)))
-
-    if checks:
-        run_checks_scipy(d_1, d_2, d_3, d_4)
-
-    return d_1, d_2, d_3, d_4
-
-
-def generate_3d_product_code(
-    a_1: csr_matrix, a_2: csr_matrix, p: csr_matrix
-) -> tuple[csr_matrix, csr_matrix, csr_matrix]:
-    """Generate 3D HGP code."""
-    r, c = p.shape
-
-    id_r = sparse.identity(r, dtype=int)
-    id_c = sparse.identity(c, dtype=int)
-    id_n0 = sparse.identity(a_1.shape[0], dtype=int)
-    id_n1 = sparse.identity(a_2.shape[0], dtype=int)
-    id_n2 = sparse.identity(a_2.shape[1], dtype=int)
-
-    d_1 = sparse.hstack((sparse.kron(a_1, id_r), sparse.kron(id_n0, p)))
-
-    x = sparse.hstack((sparse.kron(a_2, id_r), sparse.kron(id_n1, p)))
-    y = sparse.kron(a_1, id_c)
-    dims = (y.shape[0], x.shape[1] - y.shape[1])
-    z = sparse.hstack((csr_matrix(np.zeros(dims), dtype=int), y))
-    d_2 = sparse.vstack((x, z))
-
-    d_3 = sparse.vstack((sparse.kron(id_n2, p), sparse.kron(a_2, id_c)))
-
-    if not (sparse_all_zeros(d_1 @ d_2) and sparse_all_zeros(d_2 @ d_3)):
-        msg = "Error generating 3D code, boundary maps do not square to zero"
-        raise RuntimeError(msg)
-
-    return d_1, d_2, d_3  # mx, hx, hzT # hx, hzT, mzT
-
-
 def create_outpath(codename: str) -> str:
     """Create output path for code."""
     path = f"/codes/generated_codes/{codename}/"
@@ -203,7 +116,7 @@ def create_code(
     # Extend to 3D HGP
     a1 = sparse.csr_matrix(code.hx)
     a2 = sparse.csr_matrix(code.hz.T)
-    res = generate_3d_product_code(a1, a2, sparse.csr_matrix(seed_codes[2]))
+    res = generate_sparse_3d_product_code(a1, a2, sparse.csr_matrix(seed_codes[2]))
     hx, hz_t, mz_t = res
 
     hz = hz_t.transpose()
diff --git a/src/mqt/qecc/cc_decoder/__init__.py b/src/mqt/qecc/cc_decoder/__init__.py
index 14fab6efc..8eb489f0e 100644
--- a/src/mqt/qecc/cc_decoder/__init__.py
+++ b/src/mqt/qecc/cc_decoder/__init__.py
@@ -9,9 +9,9 @@
 
 from __future__ import annotations
 
-from ..codes.color_code import ColorCode, LatticeType
-from ..codes.hexagonal_color_code import HexagonalColorCode
-from ..codes.square_octagon_color_code import SquareOctagonColorCode
+from ..codes.constructions.color_codes.color_code import ColorCode, LatticeType
+from ..codes.constructions.color_codes.hexagonal_color_code import HexagonalColorCode
+from ..codes.constructions.color_codes.square_octagon_color_code import SquareOctagonColorCode
 from .comparison import tn_decoder
 from .utils import code_from_string
 
diff --git a/src/mqt/qecc/cc_decoder/decoder.py b/src/mqt/qecc/cc_decoder/decoder.py
index 05c304e60..2a7cfd013 100644
--- a/src/mqt/qecc/cc_decoder/decoder.py
+++ b/src/mqt/qecc/cc_decoder/decoder.py
@@ -26,7 +26,7 @@
     import numpy.typing as npt
     from z3 import BoolRef, ModelRef
 
-    from ..codes.color_code import ColorCode
+    from ..codes.constructions.color_codes.color_code import ColorCode
 
 
 @dataclass
diff --git a/src/mqt/qecc/cc_decoder/utils.py b/src/mqt/qecc/cc_decoder/utils.py
index 057128185..77998a2f6 100644
--- a/src/mqt/qecc/cc_decoder/utils.py
+++ b/src/mqt/qecc/cc_decoder/utils.py
@@ -11,12 +11,12 @@
 
 from typing import TYPE_CHECKING
 
-from ..codes.color_code import LatticeType
-from ..codes.hexagonal_color_code import HexagonalColorCode
-from ..codes.square_octagon_color_code import SquareOctagonColorCode
+from ..codes.constructions.color_codes.color_code import LatticeType
+from ..codes.constructions.color_codes.hexagonal_color_code import HexagonalColorCode
+from ..codes.constructions.color_codes.square_octagon_color_code import SquareOctagonColorCode
 
 if TYPE_CHECKING:
-    from ..codes.color_code import ColorCode
+    from ..codes.constructions.color_codes.color_code import ColorCode
 
 
 def code_from_string(lattice_type: str, distance: int) -> ColorCode:
diff --git a/src/mqt/qecc/circuit_synthesis/circuits.py b/src/mqt/qecc/circuit_synthesis/circuits.py
index 88549ef93..55257d7f7 100644
--- a/src/mqt/qecc/circuit_synthesis/circuits.py
+++ b/src/mqt/qecc/circuit_synthesis/circuits.py
@@ -17,7 +17,7 @@
 from qiskit.transpiler.passes import RemoveResetInZeroState
 
 from ..codes import CSSCode, StabilizerCode
-from ..codes.pauli import Pauli
+from ..codes.core.pauli import Pauli
 from .circuit_utils import compose_circuits, num_two_qubit_gates, two_qubit_gate_depth
 
 if TYPE_CHECKING:  # pragma: no cover
diff --git a/src/mqt/qecc/circuit_synthesis/cnot.py b/src/mqt/qecc/circuit_synthesis/cnot.py
index 68ed91939..bc3701a69 100644
--- a/src/mqt/qecc/circuit_synthesis/cnot.py
+++ b/src/mqt/qecc/circuit_synthesis/cnot.py
@@ -19,7 +19,7 @@
 
 from mqt.qecc import mod2
 
-from ..codes.pauli import CheckMatrix
+from ..codes.core.pauli import CheckMatrix
 from .elimination import (
     CandidateGenerator,
     get_n,
diff --git a/src/mqt/qecc/circuit_synthesis/elimination.py b/src/mqt/qecc/circuit_synthesis/elimination.py
index a08a7f078..045285995 100644
--- a/src/mqt/qecc/circuit_synthesis/elimination.py
+++ b/src/mqt/qecc/circuit_synthesis/elimination.py
@@ -18,7 +18,7 @@
 import numpy as np
 import stim
 
-from ..codes.pauli import StabilizerTableau
+from ..codes.core.pauli import StabilizerTableau
 from .operations import CNOT, Swap, Transvection
 
 logger = logging.getLogger(__name__)
diff --git a/src/mqt/qecc/circuit_synthesis/encoding.py b/src/mqt/qecc/circuit_synthesis/encoding.py
index a97fc49ce..3dc8948cd 100644
--- a/src/mqt/qecc/circuit_synthesis/encoding.py
+++ b/src/mqt/qecc/circuit_synthesis/encoding.py
@@ -19,7 +19,7 @@
 from mqt.qecc import mod2
 
 from ..codes import CSSCode
-from ..codes.pauli import CheckMatrix, StabilizerTableau, complete_stabilizer_tableau_with_destabilizers
+from ..codes.core.pauli import CheckMatrix, StabilizerTableau, complete_stabilizer_tableau_with_destabilizers
 from .circuits import CliffordIsometry, CNOTCircuit
 from .exact import (
     Objective,
diff --git a/src/mqt/qecc/circuit_synthesis/exact/encoding_depth.py b/src/mqt/qecc/circuit_synthesis/exact/encoding_depth.py
index 37f0d4646..576c91349 100644
--- a/src/mqt/qecc/circuit_synthesis/exact/encoding_depth.py
+++ b/src/mqt/qecc/circuit_synthesis/exact/encoding_depth.py
@@ -27,7 +27,7 @@
 if TYPE_CHECKING:
     import numpy.typing as npt
 
-    from ...codes.pauli import CheckMatrix, StabilizerTableau
+    from ...codes.core.pauli import CheckMatrix, StabilizerTableau
     from .gate_operations import SymbolicGateOperation
 
 
diff --git a/src/mqt/qecc/circuit_synthesis/exact/encoding_gate_count.py b/src/mqt/qecc/circuit_synthesis/exact/encoding_gate_count.py
index 4c71b11f1..4cf513169 100644
--- a/src/mqt/qecc/circuit_synthesis/exact/encoding_gate_count.py
+++ b/src/mqt/qecc/circuit_synthesis/exact/encoding_gate_count.py
@@ -27,7 +27,7 @@
 if TYPE_CHECKING:
     import numpy.typing as npt
 
-    from ...codes.pauli import CheckMatrix, StabilizerTableau
+    from ...codes.core.pauli import CheckMatrix, StabilizerTableau
     from .gate_operations import SymbolicGateOperation
 
 
diff --git a/src/mqt/qecc/circuit_synthesis/exact/encoding_interface.py b/src/mqt/qecc/circuit_synthesis/exact/encoding_interface.py
index a89bd8b27..97b5c4d32 100644
--- a/src/mqt/qecc/circuit_synthesis/exact/encoding_interface.py
+++ b/src/mqt/qecc/circuit_synthesis/exact/encoding_interface.py
@@ -15,7 +15,7 @@
 import numpy as np
 import z3
 
-from ...codes.pauli import CheckMatrix, StabilizerTableau
+from ...codes.core.pauli import CheckMatrix, StabilizerTableau
 from .css_utils import determine_css_initializations
 from .encoding_depth import encode_clifford_depth, encode_css_depth
 from .encoding_gate_count import encode_clifford_gate_count, encode_css_gate_count
diff --git a/src/mqt/qecc/circuit_synthesis/exact/initialization.py b/src/mqt/qecc/circuit_synthesis/exact/initialization.py
index f9eea3a44..6b423da4a 100644
--- a/src/mqt/qecc/circuit_synthesis/exact/initialization.py
+++ b/src/mqt/qecc/circuit_synthesis/exact/initialization.py
@@ -16,7 +16,7 @@
     import numpy.typing as npt
     import z3
 
-    from ...codes.pauli import CheckMatrix, StabilizerTableau
+    from ...codes.core.pauli import CheckMatrix, StabilizerTableau
 
 
 def constrain_initial_clifford_tableau(
diff --git a/src/mqt/qecc/circuit_synthesis/exact/search.py b/src/mqt/qecc/circuit_synthesis/exact/search.py
index c7e5698e2..8619990b6 100644
--- a/src/mqt/qecc/circuit_synthesis/exact/search.py
+++ b/src/mqt/qecc/circuit_synthesis/exact/search.py
@@ -17,7 +17,7 @@
 
 from mqt.qecc import mod2
 
-from ...codes.pauli import CheckMatrix, StabilizerTableau
+from ...codes.core.pauli import CheckMatrix, StabilizerTableau
 from ..circuits import CliffordIsometry, CNOTCircuit
 from .encoding_interface import (
     CliffordDepthEncoding,
diff --git a/src/mqt/qecc/circuit_synthesis/exact/verification.py b/src/mqt/qecc/circuit_synthesis/exact/verification.py
index bf5ebe276..1585fe1ba 100644
--- a/src/mqt/qecc/circuit_synthesis/exact/verification.py
+++ b/src/mqt/qecc/circuit_synthesis/exact/verification.py
@@ -14,7 +14,7 @@
 import numpy as np
 
 from ...codes import StabilizerCode
-from ...codes.pauli import CheckMatrix, Pauli, StabilizerTableau
+from ...codes.core.pauli import CheckMatrix, Pauli, StabilizerTableau
 
 if TYPE_CHECKING:
     import numpy.typing as npt
diff --git a/src/mqt/qecc/circuit_synthesis/operations.py b/src/mqt/qecc/circuit_synthesis/operations.py
index 798d80c2c..3fbf293de 100644
--- a/src/mqt/qecc/circuit_synthesis/operations.py
+++ b/src/mqt/qecc/circuit_synthesis/operations.py
@@ -16,12 +16,12 @@
 import numpy as np
 import stim
 
-from ..codes.pauli import StabilizerTableau
+from ..codes.core.pauli import StabilizerTableau
 
 if TYPE_CHECKING:
     import numpy.typing as npt
 
-    from ..codes.pauli import CheckMatrix
+    from ..codes.core.pauli import CheckMatrix
     from .types import BinaryMatrix
 
 
diff --git a/src/mqt/qecc/circuit_synthesis/simulation.py b/src/mqt/qecc/circuit_synthesis/simulation.py
index e227de3bc..58f8df185 100644
--- a/src/mqt/qecc/circuit_synthesis/simulation.py
+++ b/src/mqt/qecc/circuit_synthesis/simulation.py
@@ -32,7 +32,7 @@
     import numpy.typing as npt
     import stim
 
-    from ..codes.css_code import CSSCode
+    from ..codes.core.css_code import CSSCode
     from .noise import NoiseModel
 
 
diff --git a/src/mqt/qecc/circuit_synthesis/simulation_det.py b/src/mqt/qecc/circuit_synthesis/simulation_det.py
index 6d68dc27d..1c98fc200 100644
--- a/src/mqt/qecc/circuit_synthesis/simulation_det.py
+++ b/src/mqt/qecc/circuit_synthesis/simulation_det.py
@@ -31,7 +31,7 @@
     from qiskit.circuit import QuantumCircuit
     from qsample.callbacks import Callback, CallbackList  # ty: ignore[unresolved-import]
 
-    from ..codes.css_code import CSSCode
+    from ..codes.core.css_code import CSSCode
     from .state_prep_det import DeterministicCorrection, DeterministicVerification
 
 
diff --git a/src/mqt/qecc/circuit_synthesis/state_prep.py b/src/mqt/qecc/circuit_synthesis/state_prep.py
index 6b848fb4b..0fba8076b 100644
--- a/src/mqt/qecc/circuit_synthesis/state_prep.py
+++ b/src/mqt/qecc/circuit_synthesis/state_prep.py
@@ -18,7 +18,7 @@
 import z3
 from qiskit.circuit import AncillaRegister, ClassicalRegister, QuantumCircuit, QuantumRegister
 
-from ..codes.pauli import CheckMatrix
+from ..codes.core.pauli import CheckMatrix
 from .circuits import CNOTCircuit
 from .encoding import cnot_encoding_circuit
 from .exact import Objective, SynthesisStatus, TargetKind, synthesize_isometry_exact
@@ -39,7 +39,7 @@
 
     import numpy.typing as npt
 
-    from ..codes.css_code import CSSCode
+    from ..codes.core.css_code import CSSCode
 
 
 class FaultyStatePrepCircuit:
diff --git a/src/mqt/qecc/circuit_synthesis/strategy.py b/src/mqt/qecc/circuit_synthesis/strategy.py
index adc203402..8c75801fc 100644
--- a/src/mqt/qecc/circuit_synthesis/strategy.py
+++ b/src/mqt/qecc/circuit_synthesis/strategy.py
@@ -15,7 +15,7 @@
 
 from mqt.qecc import mod2
 
-from ..codes.pauli import CheckMatrix, StabilizerTableau
+from ..codes.core.pauli import CheckMatrix, StabilizerTableau
 from .cnot import GreedyCNOTGenerator
 from .elimination import EliminationStrategy, ParallelFilter
 from .rollout import (
diff --git a/src/mqt/qecc/circuit_synthesis/synthesis.py b/src/mqt/qecc/circuit_synthesis/synthesis.py
index 431a6f385..761746a68 100644
--- a/src/mqt/qecc/circuit_synthesis/synthesis.py
+++ b/src/mqt/qecc/circuit_synthesis/synthesis.py
@@ -12,7 +12,7 @@
 from dataclasses import dataclass
 from typing import TYPE_CHECKING
 
-from ..codes.pauli import CheckMatrix, StabilizerTableau
+from ..codes.core.pauli import CheckMatrix, StabilizerTableau
 from . import strategy
 from .elimination import EliminationSequence, eliminate
 from .operations import CNOT
diff --git a/src/mqt/qecc/circuit_synthesis/transvection.py b/src/mqt/qecc/circuit_synthesis/transvection.py
index 1405b0d27..f5dad0649 100644
--- a/src/mqt/qecc/circuit_synthesis/transvection.py
+++ b/src/mqt/qecc/circuit_synthesis/transvection.py
@@ -17,7 +17,7 @@
 
 from mqt.qecc import mod2
 
-from ..codes.pauli import StabilizerTableau
+from ..codes.core.pauli import StabilizerTableau
 from .elimination import CandidateGenerator, EliminationSequence, get_n
 from .operations import PauliOperation, SingleQubitClifford, Swap, Transvection
 
diff --git a/src/mqt/qecc/circuit_synthesis/types.py b/src/mqt/qecc/circuit_synthesis/types.py
index e8ad19a95..34e691f34 100644
--- a/src/mqt/qecc/circuit_synthesis/types.py
+++ b/src/mqt/qecc/circuit_synthesis/types.py
@@ -9,7 +9,7 @@
 
 from __future__ import annotations
 
-from ..codes.pauli import CheckMatrix, StabilizerTableau
+from ..codes.core.pauli import CheckMatrix, StabilizerTableau
 
 # Type alias for matrices that can be used in elimination
 BinaryMatrix = CheckMatrix | StabilizerTableau
diff --git a/src/mqt/qecc/codes/__init__.py b/src/mqt/qecc/codes/__init__.py
index 6d618b68e..4e6b55cf8 100644
--- a/src/mqt/qecc/codes/__init__.py
+++ b/src/mqt/qecc/codes/__init__.py
@@ -9,15 +9,19 @@
 
 from __future__ import annotations
 
-from .bb_codes import construct_bb_code
-from .color_code import ColorCode, LatticeType
-from .concatenation import ConcatenatedCode, ConcatenatedCSSCode
-from .constructions import construct_iceberg_code, construct_many_hypercube_code, construct_quantum_hamming_code
-from .css_code import CSSCode, InvalidCSSCodeError
-from .hexagonal_color_code import HexagonalColorCode
-from .rotated_surface_code import InvalidDistanceError, RotatedSurfaceCode
-from .square_octagon_color_code import SquareOctagonColorCode
-from .stabilizer_code import InvalidStabilizerCodeError, StabilizerCode
+from .constructions.bb_codes import construct_bb_code
+from .constructions.color_codes.color_code import ColorCode, LatticeType
+from .constructions.color_codes.hexagonal_color_code import HexagonalColorCode
+from .constructions.color_codes.square_octagon_color_code import SquareOctagonColorCode
+from .constructions.concatenation import ConcatenatedCode, ConcatenatedCSSCode
+from .constructions.constructions import (
+    construct_iceberg_code,
+    construct_many_hypercube_code,
+    construct_quantum_hamming_code,
+)
+from .constructions.rotated_surface_code import InvalidDistanceError, RotatedSurfaceCode
+from .core.css_code import CSSCode, InvalidCSSCodeError
+from .core.stabilizer_code import InvalidStabilizerCodeError, StabilizerCode
 
 __all__ = [
     "CSSCode",
diff --git a/src/mqt/qecc/codes/cc_4_8_8_d5/hx.npy b/src/mqt/qecc/codes/cc_4_8_8_d5/hx.npy
deleted file mode 100644
index bad457128..000000000
Binary files a/src/mqt/qecc/codes/cc_4_8_8_d5/hx.npy and /dev/null differ
diff --git a/src/mqt/qecc/codes/cc_4_8_8_d5/hz.npy b/src/mqt/qecc/codes/cc_4_8_8_d5/hz.npy
deleted file mode 100644
index bad457128..000000000
Binary files a/src/mqt/qecc/codes/cc_4_8_8_d5/hz.npy and /dev/null differ
diff --git a/src/mqt/qecc/codes/constructions/__init__.py b/src/mqt/qecc/codes/constructions/__init__.py
new file mode 100644
index 000000000..21fcd95e4
--- /dev/null
+++ b/src/mqt/qecc/codes/constructions/__init__.py
@@ -0,0 +1,8 @@
+# Copyright (c) 2023 - 2026 Chair for Design Automation, TUM
+# All rights reserved.
+#
+# SPDX-License-Identifier: MIT
+#
+# Licensed under the MIT License
+
+"""Concrete code families and construction utilities."""
diff --git a/src/mqt/qecc/codes/bb_codes.py b/src/mqt/qecc/codes/constructions/bb_codes.py
similarity index 97%
rename from src/mqt/qecc/codes/bb_codes.py
rename to src/mqt/qecc/codes/constructions/bb_codes.py
index ff5e5405f..cee8c05f3 100644
--- a/src/mqt/qecc/codes/bb_codes.py
+++ b/src/mqt/qecc/codes/constructions/bb_codes.py
@@ -13,7 +13,7 @@
 
 import numpy as np
 
-from .css_code import CSSCode, InvalidCSSCodeError
+from ..core.css_code import CSSCode, InvalidCSSCodeError
 
 if TYPE_CHECKING:  # pragma: no cover
     import numpy.typing as npt
diff --git a/src/mqt/qecc/codes/constructions/color_codes/__init__.py b/src/mqt/qecc/codes/constructions/color_codes/__init__.py
new file mode 100644
index 000000000..cadced227
--- /dev/null
+++ b/src/mqt/qecc/codes/constructions/color_codes/__init__.py
@@ -0,0 +1,8 @@
+# Copyright (c) 2023 - 2026 Chair for Design Automation, TUM
+# All rights reserved.
+#
+# SPDX-License-Identifier: MIT
+#
+# Licensed under the MIT License
+
+"""Color codes and their constructions."""
diff --git a/src/mqt/qecc/codes/color_code.py b/src/mqt/qecc/codes/constructions/color_codes/color_code.py
similarity index 98%
rename from src/mqt/qecc/codes/color_code.py
rename to src/mqt/qecc/codes/constructions/color_codes/color_code.py
index 1cb95c5f2..b80deb6e2 100644
--- a/src/mqt/qecc/codes/color_code.py
+++ b/src/mqt/qecc/codes/constructions/color_codes/color_code.py
@@ -14,7 +14,7 @@
 
 import numpy as np
 
-from .css_code import CSSCode
+from ...core.css_code import CSSCode
 
 if TYPE_CHECKING:
     import numpy.typing as npt
diff --git a/src/mqt/qecc/codes/hexagonal_color_code.py b/src/mqt/qecc/codes/constructions/color_codes/hexagonal_color_code.py
similarity index 100%
rename from src/mqt/qecc/codes/hexagonal_color_code.py
rename to src/mqt/qecc/codes/constructions/color_codes/hexagonal_color_code.py
diff --git a/src/mqt/qecc/codes/square_octagon_color_code.py b/src/mqt/qecc/codes/constructions/color_codes/square_octagon_color_code.py
similarity index 100%
rename from src/mqt/qecc/codes/square_octagon_color_code.py
rename to src/mqt/qecc/codes/constructions/color_codes/square_octagon_color_code.py
diff --git a/src/mqt/qecc/codes/concatenation.py b/src/mqt/qecc/codes/constructions/concatenation.py
similarity index 97%
rename from src/mqt/qecc/codes/concatenation.py
rename to src/mqt/qecc/codes/constructions/concatenation.py
index 32e147e80..07d462af8 100644
--- a/src/mqt/qecc/codes/concatenation.py
+++ b/src/mqt/qecc/codes/constructions/concatenation.py
@@ -14,10 +14,10 @@
 
 import numpy as np
 
-from .css_code import CSSCode
-from .pauli import Pauli
-from .stabilizer_code import InvalidStabilizerCodeError, StabilizerCode
-from .symplectic import SymplecticVector
+from ..core.css_code import CSSCode
+from ..core.pauli import Pauli
+from ..core.stabilizer_code import InvalidStabilizerCodeError, StabilizerCode
+from ..core.symplectic import SymplecticVector
 
 if TYPE_CHECKING:
     import numpy.typing as npt
diff --git a/src/mqt/qecc/codes/constructions.py b/src/mqt/qecc/codes/constructions/constructions.py
similarity index 98%
rename from src/mqt/qecc/codes/constructions.py
rename to src/mqt/qecc/codes/constructions/constructions.py
index 87ab2cef5..c4b574b44 100644
--- a/src/mqt/qecc/codes/constructions.py
+++ b/src/mqt/qecc/codes/constructions/constructions.py
@@ -13,7 +13,7 @@
 
 import numpy as np
 
-from .css_code import CSSCode
+from ..core.css_code import CSSCode
 
 if TYPE_CHECKING:
     import numpy.typing as npt
diff --git a/src/mqt/qecc/codes/constructions/hypergraph_product_code.py b/src/mqt/qecc/codes/constructions/hypergraph_product_code.py
new file mode 100644
index 000000000..6c2a31048
--- /dev/null
+++ b/src/mqt/qecc/codes/constructions/hypergraph_product_code.py
@@ -0,0 +1,259 @@
+# Copyright (c) 2023 - 2026 Chair for Design Automation, TUM
+# All rights reserved.
+#
+# SPDX-License-Identifier: MIT
+#
+# Licensed under the MIT License
+
+"""Hypergraph product code constructions (3D and 4D, dense and sparse)."""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING
+
+import numpy as np
+import scipy.sparse as scs
+from scipy import sparse
+from scipy.sparse import csr_matrix
+
+if TYPE_CHECKING:
+    from numpy.typing import NDArray
+
+
+def _is_all_zeros(array: NDArray[np.int32]) -> bool:
+    """Check if array is all zeros."""
+    return not np.any(array)
+
+
+def _sparse_all_zeros(mat: csr_matrix) -> bool:
+    """Check if a sparse matrix is all zeros over GF(2), without mutating it."""
+    return not np.any(mat.data % 2)
+
+
+def _run_sparse_checks_scipy(d_1: csr_matrix, d_2: csr_matrix, d_3: csr_matrix, d_4: csr_matrix) -> None:
+    """Run checks on the boundary maps."""
+    if not (_sparse_all_zeros(d_1 @ d_2) and _sparse_all_zeros(d_2 @ d_3) and _sparse_all_zeros(d_3 @ d_4)):
+        msg = "Error generating 4D code, boundary maps do not square to zero"
+        raise RuntimeError(msg)
+
+
+def _run_checks_scipy(
+    d_1: NDArray[np.int32], d_2: NDArray[np.int32], d_3: NDArray[np.int32], d_4: NDArray[np.int32]
+) -> None:
+    """Run checks on the boundary maps."""
+    sd_1 = scs.csr_matrix(d_1)
+    sd_2 = scs.csr_matrix(d_2)
+    sd_3 = scs.csr_matrix(d_3)
+    sd_4 = scs.csr_matrix(d_4)
+
+    if not (_sparse_all_zeros(sd_1 @ sd_2) and _sparse_all_zeros(sd_2 @ sd_3) and _sparse_all_zeros(sd_3 @ sd_4)):
+        msg = "Error generating 4D code, boundary maps do not square to zero"
+        raise RuntimeError(msg)
+
+
+def generate_4d_product_code(
+    a_1: NDArray[np.int32],
+    a_2: NDArray[np.int32],
+    a_3: NDArray[np.int32],
+    p: NDArray[np.int32],
+    *,
+    checks: bool = True,
+) -> tuple[NDArray[np.int32], NDArray[np.int32], NDArray[np.int32], NDArray[np.int32]]:
+    """Generate the boundary maps of a 4D hypergraph product code (dense).
+
+    Builds the 4D chain complex from the boundary maps ``a_1, a_2, a_3`` of a
+    3D input complex and a classical seed parity-check matrix ``p``. The inputs
+    must be compatible, i.e. consecutive maps compose to zero over GF(2).
+
+    Args:
+        a_1: First boundary map of the 3D input complex.
+        a_2: Second boundary map of the 3D input complex.
+        a_3: Third boundary map of the 3D input complex.
+        p: Parity-check matrix of the classical seed code.
+        checks: If ``True``, verify that the resulting boundary maps square to
+            zero over GF(2).
+
+    Returns:
+        The four boundary maps ``(mx, hx, hz^T, mz^T)`` of the 4D complex.
+
+    Raises:
+        RuntimeError: If ``checks`` is enabled and the boundary maps do not
+            square to zero.
+    """
+    r, c = p.shape
+    id_r: NDArray[np.int32] = np.identity(r, dtype=np.int32)
+    id_c: NDArray[np.int32] = np.identity(c, dtype=np.int32)
+    id_n0: NDArray[np.int32] = np.identity(a_1.shape[0], dtype=np.int32)
+    id_n1: NDArray[np.int32] = np.identity(a_2.shape[0], dtype=np.int32)
+    id_n2: NDArray[np.int32] = np.identity(a_3.shape[0], dtype=np.int32)
+    id_n3: NDArray[np.int32] = np.identity(a_3.shape[1], dtype=np.int32)
+
+    d_1: NDArray[np.int32] = np.hstack((np.kron(a_1, id_r), np.kron(id_n0, p))).astype(np.int32)
+
+    x = np.hstack((np.kron(a_2, id_r), np.kron(id_n1, p)))
+    y = np.kron(a_1, id_c)
+    dims = (y.shape[0], x.shape[1] - y.shape[1])
+    z = np.hstack((np.zeros(dims, dtype=np.int32), y))
+    d_2 = np.vstack((x, z))
+
+    x = np.hstack((np.kron(a_3, id_r), np.kron(id_n2, p)))
+    y = np.kron(a_2, id_c)
+    dims = (y.shape[0], x.shape[1] - y.shape[1])
+    z = np.hstack((np.zeros(dims, dtype=np.int32), y))
+    d_3: NDArray[np.int32] = np.vstack((x, z)).astype(np.int32)
+
+    d_4: NDArray[np.int32] = np.vstack((np.kron(id_n3, p), np.kron(a_3, id_c)))
+
+    if checks:
+        _run_checks_scipy(d_1, d_2, d_3, d_4)
+
+    return d_1, d_2, d_3, d_4
+
+
+def generate_3d_product_code(
+    a_1: NDArray[np.int32], a_2: NDArray[np.int32], p: NDArray[np.int32]
+) -> tuple[NDArray[np.int32], NDArray[np.int32], NDArray[np.int32]]:
+    """Generate the boundary maps of a 3D hypergraph product code (dense).
+
+    Builds the 3D chain complex from the boundary maps ``a_1, a_2`` of a 2D
+    input complex and a classical seed parity-check matrix ``p``. The inputs
+    must be compatible, i.e. ``a_1 @ a_2`` is zero over GF(2).
+
+    Args:
+        a_1: First boundary map of the 2D input complex.
+        a_2: Second boundary map of the 2D input complex.
+        p: Parity-check matrix of the classical seed code.
+
+    Returns:
+        The three boundary maps ``(hx, hz^T, mz^T)`` of the 3D complex.
+
+    Raises:
+        RuntimeError: If the boundary maps do not square to zero over GF(2).
+    """
+    r, c = p.shape
+    id_r: NDArray[np.int32] = np.identity(r, dtype=np.int32)
+    id_c: NDArray[np.int32] = np.identity(c, dtype=np.int32)
+    id_n0: NDArray[np.int32] = np.identity(a_1.shape[0], dtype=np.int32)
+    id_n1: NDArray[np.int32] = np.identity(a_2.shape[0], dtype=np.int32)
+    id_n2: NDArray[np.int32] = np.identity(a_2.shape[1], dtype=np.int32)
+
+    d_1: NDArray[np.int32] = np.hstack((np.kron(a_1, id_r), np.kron(id_n0, p)))
+
+    x = np.hstack((np.kron(a_2, id_r), np.kron(id_n1, p)))
+    y = np.kron(a_1, id_c)
+    dims = (y.shape[0], x.shape[1] - y.shape[1])
+    z = np.hstack((np.zeros(dims, dtype=np.int32), y))
+    d_2: NDArray[np.int32] = np.vstack((x, z))
+
+    d_3: NDArray[np.int32] = np.vstack((np.kron(id_n2, p), np.kron(a_2, id_c)))
+
+    if not (_is_all_zeros(d_1 @ d_2 % 2) and _is_all_zeros(d_2 @ d_3 % 2)):
+        msg = "Error generating 3D code, boundary maps do not square to zero"
+        raise RuntimeError(msg)
+
+    return d_1, d_2, d_3
+
+
+def generate_sparse_4d_product_code(
+    a_1: csr_matrix,
+    a_2: csr_matrix,
+    a_3: csr_matrix,
+    p: csr_matrix,
+    *,
+    checks: bool = True,
+) -> tuple[csr_matrix, csr_matrix, csr_matrix, csr_matrix]:
+    """Generate the boundary maps of a 4D hypergraph product code (sparse).
+
+    Sparse counterpart of :func:`generate_4d_product_code`; see there for the
+    input requirements.
+
+    Args:
+        a_1: First boundary map of the 3D input complex.
+        a_2: Second boundary map of the 3D input complex.
+        a_3: Third boundary map of the 3D input complex.
+        p: Parity-check matrix of the classical seed code.
+        checks: If ``True``, verify that the resulting boundary maps square to
+            zero over GF(2).
+
+    Returns:
+        The four boundary maps ``(mx, hx, hz^T, mz^T)`` of the 4D complex.
+
+    Raises:
+        RuntimeError: If ``checks`` is enabled and the boundary maps do not
+            square to zero.
+    """
+    r, c = p.shape
+
+    id_r = sparse.identity(r, dtype=np.int32)
+    id_c = sparse.identity(c, dtype=np.int32)
+    id_n0 = sparse.identity(a_1.shape[0], dtype=np.int32)
+    id_n1 = sparse.identity(a_2.shape[0], dtype=np.int32)
+    id_n2 = sparse.identity(a_3.shape[0], dtype=np.int32)
+    id_n3 = sparse.identity(a_3.shape[1], dtype=np.int32)
+
+    d_1 = sparse.hstack((sparse.kron(a_1, id_r), sparse.kron(id_n0, p)))
+
+    x = sparse.hstack((sparse.kron(a_2, id_r), sparse.kron(id_n1, p)))
+    y = sparse.kron(a_1, id_c)
+    dims = (y.shape[0], x.shape[1] - y.shape[1])
+    nmat = csr_matrix(dims, dtype=np.int32)
+    z = sparse.hstack((nmat, y))
+    d_2 = sparse.vstack((x, z))
+
+    x = sparse.hstack((sparse.kron(a_3, id_r), sparse.kron(id_n2, p)))
+    y = sparse.kron(a_2, id_c)
+    dims = (y.shape[0], x.shape[1] - y.shape[1])
+    mat = csr_matrix(dims, dtype=np.int32)
+    z = sparse.hstack([mat, y])
+    d_3 = sparse.vstack((x, z))
+
+    d_4 = sparse.vstack((sparse.kron(id_n3, p), sparse.kron(a_3, id_c)))
+
+    if checks:
+        _run_sparse_checks_scipy(d_1, d_2, d_3, d_4)
+
+    return d_1, d_2, d_3, d_4
+
+
+def generate_sparse_3d_product_code(
+    a_1: csr_matrix, a_2: csr_matrix, p: csr_matrix
+) -> tuple[csr_matrix, csr_matrix, csr_matrix]:
+    """Generate the boundary maps of a 3D hypergraph product code (sparse).
+
+    Sparse counterpart of :func:`generate_3d_product_code`; see there for the
+    input requirements.
+
+    Args:
+        a_1: First boundary map of the 2D input complex.
+        a_2: Second boundary map of the 2D input complex.
+        p: Parity-check matrix of the classical seed code.
+
+    Returns:
+        The three boundary maps ``(hx, hz^T, mz^T)`` of the 3D complex.
+
+    Raises:
+        RuntimeError: If the boundary maps do not square to zero over GF(2).
+    """
+    r, c = p.shape
+
+    id_r = sparse.identity(r, dtype=np.int32)
+    id_c = sparse.identity(c, dtype=np.int32)
+    id_n0 = sparse.identity(a_1.shape[0], dtype=np.int32)
+    id_n1 = sparse.identity(a_2.shape[0], dtype=np.int32)
+    id_n2 = sparse.identity(a_2.shape[1], dtype=np.int32)
+
+    d_1 = sparse.hstack((sparse.kron(a_1, id_r), sparse.kron(id_n0, p)))
+
+    x = sparse.hstack((sparse.kron(a_2, id_r), sparse.kron(id_n1, p)))
+    y = sparse.kron(a_1, id_c)
+    dims = (y.shape[0], x.shape[1] - y.shape[1])
+    z = sparse.hstack((csr_matrix(dims, dtype=np.int32), y))
+    d_2 = sparse.vstack((x, z))
+
+    d_3 = sparse.vstack((sparse.kron(id_n2, p), sparse.kron(a_2, id_c)))
+
+    if not (_sparse_all_zeros(d_1 @ d_2) and _sparse_all_zeros(d_2 @ d_3)):
+        msg = "Error generating 3D code, boundary maps do not square to zero"
+        raise RuntimeError(msg)
+
+    return d_1, d_2, d_3  # hx, hz^T, mz^T
diff --git a/src/mqt/qecc/codes/rotated_surface_code.py b/src/mqt/qecc/codes/constructions/rotated_surface_code.py
similarity index 98%
rename from src/mqt/qecc/codes/rotated_surface_code.py
rename to src/mqt/qecc/codes/constructions/rotated_surface_code.py
index ca888e2d0..0d570d151 100644
--- a/src/mqt/qecc/codes/rotated_surface_code.py
+++ b/src/mqt/qecc/codes/constructions/rotated_surface_code.py
@@ -13,7 +13,7 @@
 
 import numpy as np
 
-from .css_code import CSSCode
+from ..core.css_code import CSSCode
 
 if TYPE_CHECKING:
     from numpy.typing import NDArray
diff --git a/src/mqt/qecc/codes/core/__init__.py b/src/mqt/qecc/codes/core/__init__.py
new file mode 100644
index 000000000..5e2c26694
--- /dev/null
+++ b/src/mqt/qecc/codes/core/__init__.py
@@ -0,0 +1,8 @@
+# Copyright (c) 2023 - 2026 Chair for Design Automation, TUM
+# All rights reserved.
+#
+# SPDX-License-Identifier: MIT
+#
+# Licensed under the MIT License
+
+"""Core representations for quantum error-correcting codes."""
diff --git a/src/mqt/qecc/codes/css_code.py b/src/mqt/qecc/codes/core/css_code.py
similarity index 92%
rename from src/mqt/qecc/codes/css_code.py
rename to src/mqt/qecc/codes/core/css_code.py
index 1029887d3..19fff8c95 100644
--- a/src/mqt/qecc/codes/css_code.py
+++ b/src/mqt/qecc/codes/core/css_code.py
@@ -186,7 +186,7 @@ def get_trivial_code(cls, n: int) -> CSSCode:
         return CSSCode(None, None, 1, n=n)
 
     @staticmethod
-    def from_code_name(code_name: str, distance: int | None = None) -> CSSCode:
+    def from_code_name(code_name: str) -> CSSCode:
         r"""Return CSSCode object for a known code.
 
         The following codes are supported:
@@ -194,25 +194,18 @@ def from_code_name(code_name: str, distance: int | None = None) -> CSSCode:
         - [[15, 1, 3]] tetrahedral code (\"Tetrahedral\")
         - [[9, 1, 3]] Shore code (\"Shor\")
         - [[12, 2, 4]] Carbon Code (\"Carbon\")
-        - [[9, 1, 3]] rotated surface code (\"Surface, 3\"), also default when no distance is given
-        - [[25, 1, 5]] rotated surface code (\"Surface, 5\")
-        - [[15, 7, 3]] Hamming code (\"Hamming\")
         - [[23, 1, 7]] golay code (\"Golay\")
 
         Args:
             code_name: The name of the code.
-            distance: The distance of the code.
         """
-        prefix = (Path(__file__) / "../").resolve()
+        prefix = (Path(__file__) / "../../instances/").resolve()
         paths = {
             "steane": prefix / "steane/",
             "tetrahedral": prefix / "tetrahedral/",
             "shor": prefix / "shor/",
-            "surface_3": prefix / "rotated_surface_d3/",
-            "surface_5": prefix / "rotated_surface_d5/",
             "golay": prefix / "golay/",
             "carbon": prefix / "carbon/",
-            "hamming": prefix / "hamming_15/",
         }
 
         distances = {
@@ -220,32 +213,19 @@ def from_code_name(code_name: str, distance: int | None = None) -> CSSCode:
             "tetrahedral": (7, 3),
             "shor": (3, 3),
             "golay": (7, 7),
-            "surface_3": (3, 3),
-            "surface_5": (5, 5),
             "carbon": (4, 4),
-            "hamming": (3, 3),
         }  # X, Z distances
 
         code_name = code_name.lower()
-        if code_name == "surface":
-            if distance is None:
-                distance = 3
-            code_name += f"_{distance}"
-
-        if code_name in paths:
-            hx = np.load(paths[code_name] / "hx.npy")
-            hz = np.load(paths[code_name] / "hz.npy")
-
-            if code_name in distances:
-                x_distance, z_distance = distances[code_name]
-                distance = min(x_distance, z_distance)
-                return CSSCode(hx, hz, distance, x_distance=x_distance, z_distance=z_distance)
-
-            if distance is None:
-                msg = f"Distance is not specified for {code_name}"
-                raise InvalidCSSCodeError(msg)
-        msg = f"Unknown code name: {code_name}"
-        raise InvalidCSSCodeError(msg)
+        if code_name not in paths:
+            msg = f"Unknown code name: {code_name}"
+            raise InvalidCSSCodeError(msg)
+
+        hx = np.load(paths[code_name] / "hx.npy")
+        hz = np.load(paths[code_name] / "hz.npy")
+        x_distance, z_distance = distances[code_name]
+        distance = min(x_distance, z_distance)
+        return CSSCode(hx, hz, distance, x_distance=x_distance, z_distance=z_distance)
 
     @classmethod
     def from_file(cls, file_path: str | Path) -> CSSCode:
diff --git a/src/mqt/qecc/codes/pauli.py b/src/mqt/qecc/codes/core/pauli.py
similarity index 100%
rename from src/mqt/qecc/codes/pauli.py
rename to src/mqt/qecc/codes/core/pauli.py
diff --git a/src/mqt/qecc/codes/stabilizer_code.py b/src/mqt/qecc/codes/core/stabilizer_code.py
similarity index 99%
rename from src/mqt/qecc/codes/stabilizer_code.py
rename to src/mqt/qecc/codes/core/stabilizer_code.py
index 34753a6d1..d6861bfb8 100644
--- a/src/mqt/qecc/codes/stabilizer_code.py
+++ b/src/mqt/qecc/codes/core/stabilizer_code.py
@@ -21,7 +21,7 @@
 if TYPE_CHECKING:
     import numpy.typing as npt
 
-    from mqt.qecc.codes.symplectic import SymplecticVector
+    from mqt.qecc.codes.core.symplectic import SymplecticVector
 
 
 class StabilizerCode:
diff --git a/src/mqt/qecc/codes/symplectic.py b/src/mqt/qecc/codes/core/symplectic.py
similarity index 100%
rename from src/mqt/qecc/codes/symplectic.py
rename to src/mqt/qecc/codes/core/symplectic.py
diff --git a/src/mqt/qecc/codes/hamming_15/hx.npy b/src/mqt/qecc/codes/hamming_15/hx.npy
deleted file mode 100644
index eb25185f2..000000000
Binary files a/src/mqt/qecc/codes/hamming_15/hx.npy and /dev/null differ
diff --git a/src/mqt/qecc/codes/hamming_15/hz.npy b/src/mqt/qecc/codes/hamming_15/hz.npy
deleted file mode 100644
index eb25185f2..000000000
Binary files a/src/mqt/qecc/codes/hamming_15/hz.npy and /dev/null differ
diff --git a/src/mqt/qecc/codes/instances/README.md b/src/mqt/qecc/codes/instances/README.md
new file mode 100644
index 000000000..2ae08d32a
--- /dev/null
+++ b/src/mqt/qecc/codes/instances/README.md
@@ -0,0 +1,41 @@
+# Hard-coded code instances
+
+This directory holds concrete quantum error-correcting code instances that ship
+with the package because they cannot (easily) be generated on the fly or are
+convenient to have immediately available. It is the `instances/` layer of
+`mqt.qecc.codes` (see also `core/` and `constructions/`).
+
+## Named CSS codes
+
+Each of the following sub-directories stores a code as two NumPy arrays,
+`hx.npy` and `hz.npy` (the X- and Z-check matrices):
+
+| Directory      | Code                       |
+| -------------- | -------------------------- |
+| `steane/`      | `[[7, 1, 3]]` Steane       |
+| `shor/`        | `[[9, 1, 3]]` Shor         |
+| `tetrahedral/` | `[[15, 1, 3]]` tetrahedral |
+| `carbon/`      | `[[12, 2, 4]]` carbon      |
+| `golay/`       | `[[23, 1, 7]]` Golay       |
+
+These are the codes returned by `CSSCode.from_code_name(...)`, e.g.
+`CSSCode.from_code_name("Steane")`.
+
+## `lifted_product/`
+
+Pre-generated check matrices for lifted-product codes, stored as sparse
+`.npz` arrays. File names follow `lp_l=<lift>_h{x,z}.npz`.
+
+## `misc/`
+
+Example codes stored in the human-readable text formats accepted by
+`CSSCode.from_file(...)`. They double as fixtures for the supported formats:
+
+| File         | Format                                               |
+| ------------ | ---------------------------------------------------- |
+| `8_3_3.txt`  | Pauli-string stabilizers (one per line)              |
+| `15_3_5.txt` | Python list notation (`[[1,0,...], ...]`)            |
+| `30_6_5.txt` | NumPy-array notation (space-separated `[[1 0 ...]]`) |
+
+File names follow the `n_k_d` convention (physical qubits, logical qubits,
+distance).
diff --git a/src/mqt/qecc/codes/carbon/hx.npy b/src/mqt/qecc/codes/instances/carbon/hx.npy
similarity index 100%
rename from src/mqt/qecc/codes/carbon/hx.npy
rename to src/mqt/qecc/codes/instances/carbon/hx.npy
diff --git a/src/mqt/qecc/codes/carbon/hz.npy b/src/mqt/qecc/codes/instances/carbon/hz.npy
similarity index 100%
rename from src/mqt/qecc/codes/carbon/hz.npy
rename to src/mqt/qecc/codes/instances/carbon/hz.npy
diff --git a/src/mqt/qecc/codes/golay/hx.npy b/src/mqt/qecc/codes/instances/golay/hx.npy
similarity index 100%
rename from src/mqt/qecc/codes/golay/hx.npy
rename to src/mqt/qecc/codes/instances/golay/hx.npy
diff --git a/src/mqt/qecc/codes/golay/hz.npy b/src/mqt/qecc/codes/instances/golay/hz.npy
similarity index 100%
rename from src/mqt/qecc/codes/golay/hz.npy
rename to src/mqt/qecc/codes/instances/golay/hz.npy
diff --git a/src/mqt/qecc/analog_information_decoding/codes/lifted_product/lp_l=16_hx.npz b/src/mqt/qecc/codes/instances/lifted_product/lp_l=16_hx.npz
similarity index 100%
rename from src/mqt/qecc/analog_information_decoding/codes/lifted_product/lp_l=16_hx.npz
rename to src/mqt/qecc/codes/instances/lifted_product/lp_l=16_hx.npz
diff --git a/src/mqt/qecc/analog_information_decoding/codes/lifted_product/lp_l=16_hz.npz b/src/mqt/qecc/codes/instances/lifted_product/lp_l=16_hz.npz
similarity index 100%
rename from src/mqt/qecc/analog_information_decoding/codes/lifted_product/lp_l=16_hz.npz
rename to src/mqt/qecc/codes/instances/lifted_product/lp_l=16_hz.npz
diff --git a/src/mqt/qecc/analog_information_decoding/codes/lifted_product/lp_l=21_hx.npz b/src/mqt/qecc/codes/instances/lifted_product/lp_l=21_hx.npz
similarity index 100%
rename from src/mqt/qecc/analog_information_decoding/codes/lifted_product/lp_l=21_hx.npz
rename to src/mqt/qecc/codes/instances/lifted_product/lp_l=21_hx.npz
diff --git a/src/mqt/qecc/analog_information_decoding/codes/lifted_product/lp_l=21_hz.npz b/src/mqt/qecc/codes/instances/lifted_product/lp_l=21_hz.npz
similarity index 100%
rename from src/mqt/qecc/analog_information_decoding/codes/lifted_product/lp_l=21_hz.npz
rename to src/mqt/qecc/codes/instances/lifted_product/lp_l=21_hz.npz
diff --git a/src/mqt/qecc/analog_information_decoding/codes/lifted_product/lp_l=30_hx.npz b/src/mqt/qecc/codes/instances/lifted_product/lp_l=30_hx.npz
similarity index 100%
rename from src/mqt/qecc/analog_information_decoding/codes/lifted_product/lp_l=30_hx.npz
rename to src/mqt/qecc/codes/instances/lifted_product/lp_l=30_hx.npz
diff --git a/src/mqt/qecc/analog_information_decoding/codes/lifted_product/lp_l=30_hz.npz b/src/mqt/qecc/codes/instances/lifted_product/lp_l=30_hz.npz
similarity index 100%
rename from src/mqt/qecc/analog_information_decoding/codes/lifted_product/lp_l=30_hz.npz
rename to src/mqt/qecc/codes/instances/lifted_product/lp_l=30_hz.npz
diff --git a/scripts/encoding_circuits/codes/non_css/15_3_5.txt b/src/mqt/qecc/codes/instances/misc/15_3_5.txt
similarity index 100%
rename from scripts/encoding_circuits/codes/non_css/15_3_5.txt
rename to src/mqt/qecc/codes/instances/misc/15_3_5.txt
diff --git a/scripts/encoding_circuits/codes/css/30_6_5.txt b/src/mqt/qecc/codes/instances/misc/30_6_5.txt
similarity index 100%
rename from scripts/encoding_circuits/codes/css/30_6_5.txt
rename to src/mqt/qecc/codes/instances/misc/30_6_5.txt
diff --git a/scripts/encoding_circuits/codes/non_css/8_3_3.txt b/src/mqt/qecc/codes/instances/misc/8_3_3.txt
similarity index 100%
rename from scripts/encoding_circuits/codes/non_css/8_3_3.txt
rename to src/mqt/qecc/codes/instances/misc/8_3_3.txt
diff --git a/src/mqt/qecc/codes/shor/hx.npy b/src/mqt/qecc/codes/instances/shor/hx.npy
similarity index 100%
rename from src/mqt/qecc/codes/shor/hx.npy
rename to src/mqt/qecc/codes/instances/shor/hx.npy
diff --git a/src/mqt/qecc/codes/shor/hz.npy b/src/mqt/qecc/codes/instances/shor/hz.npy
similarity index 100%
rename from src/mqt/qecc/codes/shor/hz.npy
rename to src/mqt/qecc/codes/instances/shor/hz.npy
diff --git a/src/mqt/qecc/codes/steane/hx.npy b/src/mqt/qecc/codes/instances/steane/hx.npy
similarity index 100%
rename from src/mqt/qecc/codes/steane/hx.npy
rename to src/mqt/qecc/codes/instances/steane/hx.npy
diff --git a/src/mqt/qecc/codes/steane/hz.npy b/src/mqt/qecc/codes/instances/steane/hz.npy
similarity index 100%
rename from src/mqt/qecc/codes/steane/hz.npy
rename to src/mqt/qecc/codes/instances/steane/hz.npy
diff --git a/src/mqt/qecc/codes/tetrahedral/hx.npy b/src/mqt/qecc/codes/instances/tetrahedral/hx.npy
similarity index 100%
rename from src/mqt/qecc/codes/tetrahedral/hx.npy
rename to src/mqt/qecc/codes/instances/tetrahedral/hx.npy
diff --git a/src/mqt/qecc/codes/tetrahedral/hz.npy b/src/mqt/qecc/codes/instances/tetrahedral/hz.npy
similarity index 100%
rename from src/mqt/qecc/codes/tetrahedral/hz.npy
rename to src/mqt/qecc/codes/instances/tetrahedral/hz.npy
diff --git a/src/mqt/qecc/codes/rotated_surface_d3/hx.npy b/src/mqt/qecc/codes/rotated_surface_d3/hx.npy
deleted file mode 100644
index 8fddc13b7..000000000
Binary files a/src/mqt/qecc/codes/rotated_surface_d3/hx.npy and /dev/null differ
diff --git a/src/mqt/qecc/codes/rotated_surface_d3/hz.npy b/src/mqt/qecc/codes/rotated_surface_d3/hz.npy
deleted file mode 100644
index 14ef18179..000000000
Binary files a/src/mqt/qecc/codes/rotated_surface_d3/hz.npy and /dev/null differ
diff --git a/src/mqt/qecc/codes/rotated_surface_d5/hx.npy b/src/mqt/qecc/codes/rotated_surface_d5/hx.npy
deleted file mode 100644
index b456ca419..000000000
Binary files a/src/mqt/qecc/codes/rotated_surface_d5/hx.npy and /dev/null differ
diff --git a/src/mqt/qecc/codes/rotated_surface_d5/hz.npy b/src/mqt/qecc/codes/rotated_surface_d5/hz.npy
deleted file mode 100644
index ef8c85322..000000000
Binary files a/src/mqt/qecc/codes/rotated_surface_d5/hz.npy and /dev/null differ
diff --git a/tests/analog_info/test_sparse_code_constructor.py b/tests/analog_info/test_sparse_code_constructor.py
new file mode 100644
index 000000000..613e60cb7
--- /dev/null
+++ b/tests/analog_info/test_sparse_code_constructor.py
@@ -0,0 +1,79 @@
+# Copyright (c) 2023 - 2026 Chair for Design Automation, TUM
+# All rights reserved.
+#
+# SPDX-License-Identifier: MIT
+#
+# Licensed under the MIT License
+
+"""Tests for the sparse code constructor's use of the centralized HGP builder."""
+
+from __future__ import annotations
+
+import warnings
+from types import SimpleNamespace
+from typing import TYPE_CHECKING
+
+import numpy as np
+import pytest
+from scipy.sparse import csr_matrix
+
+# `sparse_code_constructor` imports `bposd`, whose source contains invalid escape
+# sequences. These raise a DeprecationWarning (Python <= 3.11) or a SyntaxWarning
+# (>= 3.12), and the exact message wording also changed across versions; under the
+# project's ``filterwarnings = ["error"]`` config any of them would turn the import
+# into a collection error. Ignore by warning category (robust across all supported
+# Python versions) while importing the module under test.
+with warnings.catch_warnings():
+    warnings.simplefilter("ignore", DeprecationWarning)
+    warnings.simplefilter("ignore", SyntaxWarning)
+    import mqt.qecc.analog_information_decoding.code_construction.sparse_code_constructor as scc
+
+if TYPE_CHECKING:
+    from numpy.typing import NDArray
+
+
+def test_create_code_builds_valid_css_code_via_sparse_3d(monkeypatch: pytest.MonkeyPatch) -> None:
+    """`create_code` must route through `generate_sparse_3d_product_code` and yield a valid CSS code.
+
+    This pins down the wiring after the HGP builders were centralized into
+    `codes.constructions.hypergraph_product_code`: `create_code` extends the
+    seed hypergraph-product code to a 3D product code and treats the first two
+    returned boundary maps as the (Hx, Hz) of a CSS code. A valid CSS code
+    requires ``Hx @ Hz.T == 0`` over GF(2).
+
+    The bposd hypergraph product and the file/subprocess side effects are
+    stubbed out so the test is deterministic and touches neither external
+    solvers nor the filesystem.
+    """
+    # Stand in for the bposd hypergraph product with a fixed valid 2-complex
+    # (Hx @ Hz.T = 0 mod 2), so `create_code` gets well-formed boundary maps.
+    hx_seed = np.array([[1, 1]], dtype=np.int32)
+    hz_seed = np.array([[1, 1], [1, 1]], dtype=np.int32)
+    monkeypatch.setattr(scc, "hgp", lambda _h1, _h2: SimpleNamespace(hx=hx_seed, hz=hz_seed))
+
+    captured: dict[str, NDArray[np.int32]] = {}
+
+    def _capture(hx: NDArray[np.int32], hz: NDArray[np.int32], _codename: str) -> None:
+        captured["hx"] = np.asarray(hx)
+        captured["hz"] = np.asarray(hz)
+
+    # Redirect the terminal write step so nothing is persisted to disk.
+    monkeypatch.setattr(scc, "_store_code_params", _capture)
+
+    p = csr_matrix(np.array([[1, 1]], dtype=np.int32))
+    # seed_codes[0:2] are consumed by the stubbed `hgp`; seed_codes[2] (`p`) drives the
+    # 3D extension. Pass them all as csr_matrix to match the `list[csr_matrix]` signature.
+    scc.create_code("hgp", [csr_matrix(hx_seed), csr_matrix(hz_seed), p], "unit_test_code")
+
+    hx, hz = captured["hx"], captured["hz"]
+    assert hx.size > 0
+    assert hx.shape[1] == hz.shape[1]
+    # The extended code must be a valid CSS code.
+    assert not np.any((hx @ hz.T) % 2)
+
+
+def test_create_code_rejects_unknown_constructor() -> None:
+    """An unsupported constructor name must raise a clear error."""
+    p = csr_matrix(np.array([[1, 1]], dtype=np.int32))
+    with pytest.raises(ValueError, match="not implemented"):
+        scc.create_code("not_a_constructor", [p, p, p], "unit_test_code")
diff --git a/tests/circuit_synthesis/exact/conftest.py b/tests/circuit_synthesis/exact/conftest.py
index 26f465f66..a5e5328ee 100644
--- a/tests/circuit_synthesis/exact/conftest.py
+++ b/tests/circuit_synthesis/exact/conftest.py
@@ -12,7 +12,7 @@
 import numpy as np
 import pytest
 
-from mqt.qecc.codes.pauli import CheckMatrix, StabilizerTableau
+from mqt.qecc.codes.core.pauli import CheckMatrix, StabilizerTableau
 
 
 @pytest.fixture
diff --git a/tests/circuit_synthesis/exact/test_cz_gate.py b/tests/circuit_synthesis/exact/test_cz_gate.py
index 93665b3e6..a47c0f079 100644
--- a/tests/circuit_synthesis/exact/test_cz_gate.py
+++ b/tests/circuit_synthesis/exact/test_cz_gate.py
@@ -31,7 +31,7 @@
 from mqt.qecc.circuit_synthesis.exact.types import Objective, SynthesisStatus, TargetKind
 from mqt.qecc.circuit_synthesis.exact.vars import CliffordDepthVars, CliffordGateCountVars
 from mqt.qecc.circuit_synthesis.exact.verification import verify_stabilizer_state
-from mqt.qecc.codes.pauli import StabilizerTableau
+from mqt.qecc.codes.core.pauli import StabilizerTableau
 
 # ---------------------------------------------------------------------------
 # CZGate class
diff --git a/tests/circuit_synthesis/exact/test_search.py b/tests/circuit_synthesis/exact/test_search.py
index 53dd9b2c6..c300b2772 100644
--- a/tests/circuit_synthesis/exact/test_search.py
+++ b/tests/circuit_synthesis/exact/test_search.py
@@ -20,7 +20,7 @@
     verify_css_state,
     verify_stabilizer_state,
 )
-from mqt.qecc.codes.pauli import CheckMatrix, StabilizerTableau
+from mqt.qecc.codes.core.pauli import CheckMatrix, StabilizerTableau
 
 
 @pytest.mark.parametrize(
diff --git a/tests/circuit_synthesis/exact/test_sqrt_x_gate.py b/tests/circuit_synthesis/exact/test_sqrt_x_gate.py
index df4695a70..12fd86cc9 100644
--- a/tests/circuit_synthesis/exact/test_sqrt_x_gate.py
+++ b/tests/circuit_synthesis/exact/test_sqrt_x_gate.py
@@ -21,7 +21,7 @@
 from mqt.qecc.circuit_synthesis.exact.search import synthesize_isometry_exact
 from mqt.qecc.circuit_synthesis.exact.types import Objective, SynthesisStatus, TargetKind
 from mqt.qecc.circuit_synthesis.exact.verification import verify_stabilizer_state
-from mqt.qecc.codes.pauli import StabilizerTableau
+from mqt.qecc.codes.core.pauli import StabilizerTableau
 
 # ---------------------------------------------------------------------------
 # SqrtXGate class properties
diff --git a/tests/circuit_synthesis/test_circuits.py b/tests/circuit_synthesis/test_circuits.py
index b25663c63..6aae18ebd 100644
--- a/tests/circuit_synthesis/test_circuits.py
+++ b/tests/circuit_synthesis/test_circuits.py
@@ -15,8 +15,8 @@
 from qiskit import QuantumCircuit
 
 from mqt.qecc.circuit_synthesis.circuits import CliffordIsometry, CNOTCircuit, compose_cnot_circuits
-from mqt.qecc.codes.pauli import Pauli
-from mqt.qecc.codes.stabilizer_code import StabilizerCode
+from mqt.qecc.codes.core.pauli import Pauli
+from mqt.qecc.codes.core.stabilizer_code import StabilizerCode
 
 
 def test_add_cnot():
diff --git a/tests/circuit_synthesis/test_cnot.py b/tests/circuit_synthesis/test_cnot.py
index fa81e84d3..4a8b6b117 100644
--- a/tests/circuit_synthesis/test_cnot.py
+++ b/tests/circuit_synthesis/test_cnot.py
@@ -11,7 +11,7 @@
 import pytest
 
 from mqt.qecc.circuit_synthesis.synthesis import SynthesisConfig, synthesize_cnot
-from mqt.qecc.codes.pauli import CheckMatrix
+from mqt.qecc.codes.core.pauli import CheckMatrix
 
 
 @pytest.fixture
diff --git a/tests/circuit_synthesis/test_deterministic.py b/tests/circuit_synthesis/test_deterministic.py
index 4362141d5..5b0f946ac 100644
--- a/tests/circuit_synthesis/test_deterministic.py
+++ b/tests/circuit_synthesis/test_deterministic.py
@@ -17,6 +17,7 @@
 
 from mqt.qecc import CSSCode
 from mqt.qecc.circuit_synthesis import CNOTCircuit, DeterministicVerificationHelper, FaultyStatePrepCircuit
+from mqt.qecc.codes import RotatedSurfaceCode
 
 from .utils import in_span
 
@@ -77,7 +78,7 @@ def verified_steane_data(
 @pytest.fixture(scope="module")
 def surface_code_sp_zero() -> FaultyStatePrepCircuit:
     """Return a non-ft state preparation circuit for the d=3 rotated surface code."""
-    surface_code = CSSCode.from_code_name("surface", 3)
+    surface_code = RotatedSurfaceCode(3)
     sp_circ = FaultyStatePrepCircuit(
         CNOTCircuit.from_stim_circuit(
             stim.Circuit(
@@ -295,7 +296,7 @@ def test_surface_det_simulation(
     """Test simulated logical error rate for deterministic Steane state preparation."""
     verify_x_opt, verify_z_opt, verify_x_global, verify_z_global = verified_surface_data
 
-    code = CSSCode.from_code_name("surface", 3)
+    code = RotatedSurfaceCode(3)
     for verify_x, verify_z in zip((verify_x_opt, verify_x_global), (verify_z_opt, verify_z_global), strict=False):
         simulator = NoisyDFTStatePrepSimulator(
             surface_code_sp_zero.circ.to_qiskit_circuit(), (verify_x, verify_z), code, err_model, True
diff --git a/tests/circuit_synthesis/test_elimination.py b/tests/circuit_synthesis/test_elimination.py
index 1a6a79f5d..6cdd29799 100644
--- a/tests/circuit_synthesis/test_elimination.py
+++ b/tests/circuit_synthesis/test_elimination.py
@@ -13,7 +13,7 @@
 
 from mqt.qecc.circuit_synthesis.elimination import EliminationSequence
 from mqt.qecc.circuit_synthesis.operations import CNOT, Swap, Transvection
-from mqt.qecc.codes.pauli import CheckMatrix, StabilizerTableau
+from mqt.qecc.codes.core.pauli import CheckMatrix, StabilizerTableau
 
 
 @pytest.fixture
diff --git a/tests/circuit_synthesis/test_encoder_synthesis.py b/tests/circuit_synthesis/test_encoder_synthesis.py
index 1475f5d94..0ba9da78a 100644
--- a/tests/circuit_synthesis/test_encoder_synthesis.py
+++ b/tests/circuit_synthesis/test_encoder_synthesis.py
@@ -31,8 +31,14 @@
     synthesize_encoding_circuit,
 )
 from mqt.qecc.circuit_synthesis.synthesis import SynthesisConfig
-from mqt.qecc.codes import CSSCode, SquareOctagonColorCode, StabilizerCode, construct_quantum_hamming_code
-from mqt.qecc.codes.pauli import Pauli, StabilizerTableau
+from mqt.qecc.codes import (
+    CSSCode,
+    RotatedSurfaceCode,
+    SquareOctagonColorCode,
+    StabilizerCode,
+    construct_quantum_hamming_code,
+)
+from mqt.qecc.codes.core.pauli import Pauli, StabilizerTableau
 
 if TYPE_CHECKING:
     from typing import Literal
@@ -47,7 +53,7 @@ def steane_code() -> CSSCode:
 @pytest.fixture
 def surface_3() -> CSSCode:
     """Return the surface code."""
-    return CSSCode.from_code_name("surface", 3)
+    return RotatedSurfaceCode(3)
 
 
 @pytest.fixture
@@ -59,7 +65,7 @@ def tetrahedral() -> CSSCode:
 @pytest.fixture
 def hamming() -> CSSCode:
     """Return the Hamming code."""
-    return CSSCode.from_code_name("Hamming")
+    return construct_quantum_hamming_code(4)
 
 
 @pytest.fixture
@@ -376,7 +382,7 @@ def test_logical_mapping_non_css() -> None:
 
 def test_logical_mapping_css() -> None:
     """Test that logical to input mapping is correct for CSS codes."""
-    code = CSSCode.from_code_name("Hamming")
+    code = construct_quantum_hamming_code(4)
     encoder = synthesize_encoding_circuit(code)
     mapping = encoder.logical_to_input_mapping(code)
 
diff --git a/tests/circuit_synthesis/test_operations.py b/tests/circuit_synthesis/test_operations.py
index 94d495f5a..77bdae918 100644
--- a/tests/circuit_synthesis/test_operations.py
+++ b/tests/circuit_synthesis/test_operations.py
@@ -20,7 +20,7 @@
     Swap,
     Transvection,
 )
-from mqt.qecc.codes.pauli import CheckMatrix, StabilizerTableau
+from mqt.qecc.codes.core.pauli import CheckMatrix, StabilizerTableau
 
 
 @pytest.fixture
diff --git a/tests/circuit_synthesis/test_stateprep.py b/tests/circuit_synthesis/test_stateprep.py
index b14484d97..1565fc3a2 100644
--- a/tests/circuit_synthesis/test_stateprep.py
+++ b/tests/circuit_synthesis/test_stateprep.py
@@ -26,7 +26,7 @@
     heuristic_verification_circuit,
     heuristic_verification_stabilizers,
 )
-from mqt.qecc.codes import SquareOctagonColorCode
+from mqt.qecc.codes import RotatedSurfaceCode, SquareOctagonColorCode
 
 from .utils import eq_span, in_span
 
@@ -55,7 +55,7 @@ def css_6_2_2_code() -> CSSCode:
 @pytest.fixture(scope="session")
 def surface_code() -> CSSCode:
     """Return the distance 3 rotated Surface Code."""
-    return CSSCode.from_code_name("surface", 3)
+    return RotatedSurfaceCode(3)
 
 
 @pytest.fixture(scope="session")
diff --git a/tests/circuit_synthesis/test_transvection.py b/tests/circuit_synthesis/test_transvection.py
index 4a3515cca..cc00ce9f8 100644
--- a/tests/circuit_synthesis/test_transvection.py
+++ b/tests/circuit_synthesis/test_transvection.py
@@ -14,8 +14,8 @@
 from mqt.qecc.circuit_synthesis.transvection import (
     reduce_with_swaps,
 )
-from mqt.qecc.codes.pauli import StabilizerTableau
-from mqt.qecc.codes.symplectic import SymplecticMatrix
+from mqt.qecc.codes.core.pauli import StabilizerTableau
+from mqt.qecc.codes.core.symplectic import SymplecticMatrix
 
 
 @pytest.fixture
diff --git a/tests/codes/constructions/test_hypergraph_product_codes.py b/tests/codes/constructions/test_hypergraph_product_codes.py
new file mode 100644
index 000000000..30972a3c7
--- /dev/null
+++ b/tests/codes/constructions/test_hypergraph_product_codes.py
@@ -0,0 +1,121 @@
+# Copyright (c) 2023 - 2026 Chair for Design Automation, TUM
+# All rights reserved.
+#
+# SPDX-License-Identifier: MIT
+#
+# Licensed under the MIT License
+
+"""Test product code constructions."""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING
+
+import numpy as np
+import pytest
+from scipy.sparse import csr_matrix
+
+if TYPE_CHECKING:
+    from numpy.typing import NDArray
+
+from mqt.qecc.codes.constructions.hypergraph_product_code import (
+    generate_3d_product_code,
+    generate_4d_product_code,
+    generate_sparse_3d_product_code,
+    generate_sparse_4d_product_code,
+)
+
+
+@pytest.fixture
+def boundary_maps() -> tuple[NDArray[np.int32], NDArray[np.int32], NDArray[np.int32]]:
+    """Fixture for boundary maps."""
+    a_1 = np.array([[1, 1]], dtype=np.int32)
+    a_2 = np.array([[1, 1], [1, 1]], dtype=np.int32)
+    p = np.array([[1, 1]], dtype=np.int32)
+    return a_1, a_2, p
+
+
+def test_generate_3d_product_code(
+    boundary_maps: tuple[NDArray[np.int32], NDArray[np.int32], NDArray[np.int32]],
+) -> None:
+    """Test 3D HGP code construction."""
+    a_1, a_2, p = boundary_maps
+    d_1, d_2, d_3 = generate_3d_product_code(a_1, a_2, p)
+
+    assert np.array_equal(d_1, np.array([[1, 1, 1, 1]], dtype=np.int32))
+    assert d_2.shape == (4, 6)
+    assert d_3.shape == (6, 4)
+    assert not np.any(d_1 @ d_2 % 2)
+    assert not np.any(d_2 @ d_3 % 2)
+
+
+def test_generate_sparse_3d_product_code_matches_dense(
+    boundary_maps: tuple[NDArray[np.int32], NDArray[np.int32], NDArray[np.int32]],
+) -> None:
+    """Test sparse 3D HGP code construction against the dense construction."""
+    a_1, a_2, p = boundary_maps
+    expected = generate_3d_product_code(a_1, a_2, p)
+
+    result = generate_sparse_3d_product_code(csr_matrix(a_1), csr_matrix(a_2), csr_matrix(p))
+
+    for sparse_mat, dense_mat in zip(result, expected, strict=True):
+        assert np.array_equal(sparse_mat.toarray(), dense_mat)
+
+
+def test_generate_4d_product_code(
+    boundary_maps: tuple[NDArray[np.int32], NDArray[np.int32], NDArray[np.int32]],
+) -> None:
+    """Test 4D HGP code construction."""
+    a_1, a_2, p = boundary_maps
+    a_3 = np.array([[1], [1]], dtype=np.int32)
+
+    d_1, d_2, d_3, d_4 = generate_4d_product_code(a_1, a_2, a_3, p)
+
+    assert d_1.shape == (1, 4)
+    assert d_2.shape == (4, 6)
+    assert d_3.shape == (6, 5)
+    assert d_4.shape == (5, 2)
+    assert not np.any(d_1 @ d_2 % 2)
+    assert not np.any(d_2 @ d_3 % 2)
+    assert not np.any(d_3 @ d_4 % 2)
+
+
+def test_generate_sparse_4d_product_code_matches_dense(
+    boundary_maps: tuple[NDArray[np.int32], NDArray[np.int32], NDArray[np.int32]],
+) -> None:
+    """Test sparse 4D HGP code construction against the dense construction."""
+    a_1, a_2, p = boundary_maps
+    a_3 = np.array([[1], [1]], dtype=np.int32)
+    expected = generate_4d_product_code(a_1, a_2, a_3, p)
+
+    result = generate_sparse_4d_product_code(csr_matrix(a_1), csr_matrix(a_2), csr_matrix(a_3), csr_matrix(p))
+
+    for sparse_mat, dense_mat in zip(result, expected, strict=True):
+        assert np.array_equal(sparse_mat.toarray(), dense_mat)
+
+
+def test_generate_3d_product_code_rejects_invalid_boundary_maps() -> None:
+    """Test that invalid boundaries are rejected."""
+    a_1 = np.array([[1, 0]], dtype=np.int32)
+    a_2 = np.array([[1], [0]], dtype=np.int32)
+    p = np.array([[1]], dtype=np.int32)
+
+    with pytest.raises(RuntimeError, match="boundary maps do not square to zero"):
+        generate_3d_product_code(a_1, a_2, p)
+
+    with pytest.raises(RuntimeError, match="boundary maps do not square to zero"):
+        generate_sparse_3d_product_code(csr_matrix(a_1), csr_matrix(a_2), csr_matrix(p))
+
+
+def test_generate_4d_product_code_rejects_invalid_boundary_maps() -> None:
+    """Test that invalid boundaries are rejected."""
+    a_1 = np.array([[1, 0]], dtype=np.int32)
+    a_2 = np.array([[1], [0]], dtype=np.int32)
+    a_3 = np.array([[1], [0]], dtype=np.int32)
+    p = np.array([[1]], dtype=np.int32)
+
+    with pytest.raises(RuntimeError, match="boundary maps do not square to zero"):
+        generate_4d_product_code(a_1, a_2, a_3, p)
+
+    with pytest.raises(RuntimeError, match="boundary maps do not square to zero"):
+        generate_sparse_4d_product_code(csr_matrix(a_1), csr_matrix(a_2), csr_matrix(a_3), csr_matrix(p))
diff --git a/tests/test_code.py b/tests/test_code.py
index d5b74b087..644acf4c2 100644
--- a/tests/test_code.py
+++ b/tests/test_code.py
@@ -26,14 +26,14 @@
     construct_many_hypercube_code,
     construct_quantum_hamming_code,
 )
-from mqt.qecc.codes.pauli import (
+from mqt.qecc.codes.constructions.rotated_surface_code import InvalidDistanceError, RotatedSurfaceCode
+from mqt.qecc.codes.core.pauli import (
     InvalidPauliError,
     Pauli,
     StabilizerTableau,
     complete_stabilizer_tableau_with_destabilizers,
 )
-from mqt.qecc.codes.rotated_surface_code import InvalidDistanceError, RotatedSurfaceCode
-from mqt.qecc.codes.symplectic import SymplecticMatrix, SymplecticVector
+from mqt.qecc.codes.core.symplectic import SymplecticMatrix, SymplecticVector
 
 if TYPE_CHECKING:  # pragma: no cover
     import numpy.typing as npt