Galois-qudit BCH code[17] 

Description

True Galois-qudit stabilizer code constructed from BCH codes via either the Hermitian construction or the Galois-qudit CSS construction. Parameters can be improved by applying Steane enlargement [8].

Notes

See Ref. [9] for an overview of quantum BCH codes.

Parent

Child

  • Qubit BCH code — Galois-qudit BCH codes for \(q=2\) reduce to qubit BCH codes.

Cousins

References

[1]
S. Aly, A. Klappenecker, and P. K. Sarvepalli, “Primitive Quantum BCH Codes over Finite Fields”, (2006) arXiv:quant-ph/0501126
[2]
S. A. Aly, A. Klappenecker, and P. K. Sarvepalli, “On Quantum and Classical BCH Codes”, (2006) arXiv:quant-ph/0604102
[3]
Z. Ma et al., “On Non-binary Quantum BCH Codes”, Lecture Notes in Computer Science 675 (2006) DOI
[4]
S. A. Aly, A. Klappenecker, and P. K. Sarvepalli, “On Quantum and Classical BCH Codes”, IEEE Transactions on Information Theory 53, 1183 (2007) DOI
[5]
R. Li et al., “Hermitian dual containing BCH codes and Construction of new quantum codes”, Quantum Information and Computation 13, 21 (2013) DOI
[6]
G. G. La Guardia, “Constructions of new families of nonbinary quantum codes”, Physical Review A 80, (2009) DOI
[7]
X. Zhao et al., “Hermitian dual-containing constacyclic BCH codes and related quantum codes of length \(\frac{q^{2m}-1}{q+1}\)”, (2020) arXiv:2007.13309
[8]
G. G. La Guardia and R. Palazzo Jr., “Constructions of new families of nonbinary CSS codes”, Discrete Mathematics 310, 2935 (2010) DOI
[9]
A. Klappenecker, “Algebraic quantum coding theory”, Quantum Error Correction 307 (2013) DOI
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Zoo Code ID: galois_bch

Cite as:
“Galois-qudit BCH code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/galois_bch
BibTeX:
@incollection{eczoo_galois_bch, title={Galois-qudit BCH code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/galois_bch} }
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Cite as:

“Galois-qudit BCH code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/galois_bch

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits_galois/stabilizer/bch/galois_bch.yml.