Qubit stabilizer code constructed from a self-orthogonal binary BCH code via the CSS construction, from a Hermitian self-orthogonal quaternary BCH code via the stabilizer-over-\(GF(4)\) construction, or by taking a Euclidean self-orthogonal BCH code over \(GF(2^m)\), converting it to a binary code, and applying the CSS construction.
- Qubit stabilizer code — qubit BCH codes constructed via the CSS construction are CSS codes, and the rest are stabilizer codes over \(GF(4)\).
- Binary BCH code — Binary BCH codes are used to construct a subset of qubit BCH codes via the CSS construction.
- Bose–Chaudhuri–Hocquenghem (BCH) code — BCH codes are used to construct qubit BCH codes via the CSS and stabilizer-over-\(GF(4)\) constructions.
- Calderbank-Shor-Steane (CSS) stabilizer code — Some qubit BCH codes are CSS.
- Stabilizer code over \(GF(4)\) — Hermitian self-orthogonal quaternary BCH codes are used to construct a subset of qubit BCH codes via the stabilizer-over-\(GF(4)\) construction.
- Galois-qudit BCH code
- M. Grassl, T. Beth, and T. Pellizzari, “Codes for the quantum erasure channel”, Physical Review A 56, 33 (1997). DOI; quant-ph/9610042
- A. R. Calderbank et al., “Quantum Error Correction via Codes over GF(4)”. quant-ph/9608006
- Andrew M. Steane, “Enlargement of Calderbank Shor Steane quantum codes”. quant-ph/9802061
- Markus Grassl and Thomas Beth, “Quantum BCH Codes”. quant-ph/9910060
Zoo code information
“Qubit BCH code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quantum_bch