Here are a gigantic list of all the codes, sorted alphabetically, that were
included in the error correction zoo.
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3D surface code
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Abelian topological code
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Additive \(q\)-ary code
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Alamouti code
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Algebraic-geometry (AG) code
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Alternant code
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Approximate quantum error-correcting code (AQECC)
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Approximate secret-sharing code
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Availability code
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Bacon-Shor code
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Balanced product code
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Binary Golay code
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Binary code
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Binary permutation-based code
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Binary quantum Goppa code
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Binary repetition code
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Binomial code
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Bose–Chaudhuri–Hocquenghem (BCH) code
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Bosonic code
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Bosonic rotation code
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Bosonic stabilizer code
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Bravyi-Bacon-Shor (BBS) code
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Calderbank-Shor-Steane (CSS) stabilizer code
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Cat code
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Category-based quantum code
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Chuang-Leung-Yamamoto code
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Clifford-deformed surface code (CDSC)
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Codeword stabilized (CWS) code
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Color code
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Concatenated code
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Concatenated quantum code
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Constant-excitation (CE) code
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Constant-excitation permutation-invariant code
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Convolutional code
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Covering code
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Cyclic code
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Distance-balanced code
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Distributed-storage code
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Divisible code
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Double-semion code
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Dual linear code
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Dual-rail code
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Dynamically-generated quantum error-correcting code
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Eigenstate thermalization hypothesis (ETH) code
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Entanglement-assisted (EA) QECC
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Entanglement-assisted (EA) operator QECC
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Entanglement-assisted (EA) stabilizer code
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Entanglement-assisted hybrid classical-quantum (EACQ) code
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Error-correcting code (ECC)
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Evaluation AG code
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Expander code
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Expander lifted-product code
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Extended RS code
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Fermionic code
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Fiber-bundle code
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Fibonacci string-net code
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Finite-dimensional quantum error-correcting code
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Floquet code
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Fock-state bosonic code
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Folded RS code
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Fountain code
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Fractal surface code
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Fracton code
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Freedman-Meyer-Luo code
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Frobenius code
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Fusion-based quantum computing (FBQC) code
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GKP-stabilizer code
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GNU permutation-invariant code
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Gabidulin code
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Galois-field \(q\)-ary code
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Galois-qudit CSS code
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Galois-qudit code
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Galois-qudit non-stabilizer code
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Galois-qudit polynomial code (QPyC)
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Galois-qudit stabilizer code
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Generalized Reed-Solomon (GRS) code
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Generalized concatenated code
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Generalized homological product code
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Goppa code
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Gottesman-Kitaev-Preskill (GKP) code
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Graph homology code
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Gross spin code
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Group GKP code
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Group-based code
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Group-based quantum code
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Guth-Lubotzky code
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H code
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Haah cubic code
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Haar-random code
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Hadamard code
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Hamiltonian-based code
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Hamming code
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Heavy-hexagon code
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Higher-dimensional surface code
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Holographic code
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Homological bosonic code
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Homological product code
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Honeycomb code
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Hybrid qudit-oscillator code
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Hyperbolic surface code
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Hypergraph product code
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Identifiable parent property (IPP) code
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Justesen code
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Kitaev surface code
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Lattice-based code
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Levenshtein code
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Lifted-product (LP) code
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Linear \(q\)-ary code
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Linear binary code
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Local Haar-random circuit code
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Locally recoverable code (LRC)
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Low-density parity-check (LDPC) code
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Low-depth random Clifford-circuit code
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Luby transform (LT) code
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Majorana stabilizer code
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Matching code
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Matrix code
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Maximum distance separable (MDS) code
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Maximum-rank distance (MRD) code
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Minimum-bandwidth regenerating (MBR) code
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Minimum-storage regenerating (MSR) code
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Modular-qudit CSS code
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Modular-qudit code
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Modular-qudit stabilizer code
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Modular-qudit surface code
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Molecular code
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Monitored random-circuit code
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Movassagh-Ouyang Hamiltonian code
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Multi-mode GKP code
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Niset-Andersen-Cerf code
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Number-phase code
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Operator-algebra error-correcting code
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Orthogonal Spacetime Block Code (OSTBC)
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Oscillator-into-oscillator code
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Parallel concatenated code
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Parallel-recovery code
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Parity-check code
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Pastawski-Yoshida-Harlow-Preskill (HaPPY) code
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Perfect code
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Perfect quantum code
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Permutation-invariant code
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Polar code
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Prime-qudit polynomial code (QPyC)
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Projective-plane surface code
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Quadratic-residue code
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Quantum Lego code
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Quantum Reed-Muller code
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Quantum Tanner code
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Quantum convolutional code
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Quantum cyclic code
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Quantum divisible code
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Quantum error-correcting code (QECC)
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Quantum expander code
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Quantum low-density parity-check (QLDPC) code
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Quantum maximum-distance-separable (MDS) code
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Quantum parity code (QPC)
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Quantum polar code
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Quantum repetition code
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Quantum-double code
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Quasi-cyclic code
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Quaternary code over \(\mathbb{Z}_4\)
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Qubit code
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Qubit stabilizer code
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Qudit-into-oscillator code
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Ramanujan-complex product code
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Random code
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Random quantum code
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Random-circuit code
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Rank-metric code
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Rank-modulation code
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Raptor (RAPid TORnado) code
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Raussendorf-Bravyi-Harrington (RBH) code
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Reed-Muller (RM) code
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Reed-Solomon (RS) code
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Regenerating code (RGC)
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Residue AG code
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Ring code
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Rotor GKP code
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Self-correcting quantum code
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Sequential-recovery code
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Shor \([[9,1,3]]\) code
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Single parity-check code
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Skew-cyclic CSS code
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Skew-cyclic code
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Spacetime block code (STBC)
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Spacetime code (STC)
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Spherical code
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Spin code
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Stabilizer code
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Stabilizer code over \(GF(4)\)
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Stabilizer code over \(GF(q^2)\)
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Steane \([[7,1,3]]\) code
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String-net code
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Subsystem color code
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Subsystem quantum error-correcting code
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Subsystem qubit stabilizer code
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Symmetry-protected self-correcting quantum code
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Tanner code
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Three qutrit code
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Topological code
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Tornado code
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Translationally-invariant stabilizer code
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Transverse-field Ising model (TFIM) code
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Triorthogonal code
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True Galois-qudit stabilizer code
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Two-dimensional hyperbolic surface code
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Two-weight code
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Very small logical qubit (VSLQ) code
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Wasilewski-Banaszek code
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Wozencraft ensemble code
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XP stabilizer code
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XS stabilizer code
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XY surface code
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XYZ product code
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XYZ\(^2\) hexagonal stabilizer code
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XZZX surface code
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Zetterberg code
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\(R\)-linear code
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\([[15,1,3]]\) Reed-Muller code
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\([[2^r, 2^r-r-2, 3]]\) quantum Hamming code
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\([[2^r-1, 2^r-2r-1, 3]]\) Hamming-based CSS code
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\([[2^r-1, 2^r-2r-1, 3]]_p\) prime-qudit CSS code
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\([[4,2,2]]\) CSS code
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\([[5,1,3]]\) perfect code
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\(q\)-ary group code