Qubit BCH code[1][2][3][4]

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

References

[1]
M. Grassl, T. Beth, and T. Pellizzari, “Codes for the quantum erasure channel”, Physical Review A 56, 33 (1997). DOI; quant-ph/9610042
[2]
A. R. Calderbank et al., “Quantum Error Correction via Codes over GF(4)”. quant-ph/9608006
[3]
Andrew M. Steane, “Enlargement of Calderbank Shor Steane quantum codes”. quant-ph/9802061
[4]
Markus Grassl and Thomas Beth, “Quantum BCH Codes”. quant-ph/9910060

Zoo code information

Internal code ID: quantum_bch

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

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:
https://errorcorrectionzoo.org/c/quantum_bch

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.