Qubit BCH code[1–5] 

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.

Parents

  • Qubit stabilizer code — Qubit BCH codes constructed via the CSS construction are CSS codes, and the rest are stabilizer codes over \(GF(4)\).
  • Galois-qudit BCH code — Galois-qudit BCH codes for \(q=2\) reduce to qubit BCH codes.

Cousins

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
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Zoo Code ID: quantum_bch

Cite as:
“Qubit BCH code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quantum_bch
BibTeX:
@incollection{eczoo_quantum_bch,
  title={Qubit BCH code},
  booktitle={The Error Correction Zoo},
  year={2022},
  editor={Albert, Victor V. and Faist, Philippe},
  url={https://errorcorrectionzoo.org/c/quantum_bch}
}
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Permanent link:
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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/stabilizer/quantum_bch.yml.