Description
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.
Parent
- Qubit stabilizer code — qubit BCH codes constructed via the CSS construction are CSS codes, and the rest are stabilizer codes over \(GF(4)\).
Cousins
- 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
References
- [1]
- A. M. Steane, “Simple quantum error-correcting codes”, Physical Review A 54, 4741 (1996) arXiv:quant-ph/9605021 DOI
- [2]
- M. Grassl, Th. Beth, and T. Pellizzari, “Codes for the quantum erasure channel”, Physical Review A 56, 33 (1997) arXiv:quant-ph/9610042 DOI
- [3]
- A. R. Calderbank et al., “Quantum Error Correction via Codes over GF(4)”, (1997) arXiv:quant-ph/9608006
- [4]
- A. M. Steane, “Enlargement of Calderbank Shor Steane quantum codes”, (1998) arXiv:quant-ph/9802061
- [5]
- M. Grassl and T. Beth, “Quantum BCH Codes”, (1999) arXiv:quant-ph/9910060
Page edit log
- Victor V. Albert (2022-07-21) — most recent
Cite as:
“Qubit BCH code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quantum_bch
Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qubits/quantum_bch.yml.