Galois-qudit BCH code[1][2][3][4][5][6]

Description

True Galois-qudit stabilizer code constructed from BCH codes via either the Hermitian construction or the Galois-qudit CSS construction.

Parent

  • True Galois-qudit stabilizer code — Galois-qudit BCH codes constructed via the CSS construction are Galois-qudit CSS codes, and the rest are true stabilizer codes.

Cousins

References

[1]
Salah Aly, Andreas Klappenecker, and Pradeep Kiran Sarvepalli, “Primitive Quantum BCH Codes over Finite Fields”. quant-ph/0501126
[2]
Salah A. Aly, Andreas Klappenecker, and Pradeep Kiran Sarvepalli, “On Quantum and Classical BCH Codes”. quant-ph/0604102
[3]
S. A. Aly, A. Klappenecker, and P. K. Sarvepalli, “On Quantum and Classical BCH Codes”, IEEE Transactions on Information Theory 53, 1183 (2007). DOI
[4]
R. Li et al., “Hermitian dual containing BCH codes and Construction of new quantum codes”, Quantum Information and Computation 13, 21 (2013). DOI
[5]
G. G. La Guardia, “Constructions of new families of nonbinary quantum codes”, Physical Review A 80, (2009). DOI
[6]
X. Zhao et al., “Hermitian dual-containing constacyclic BCH codes and related quantum codes of length $\frac{q^{2m}-1}{q+1}$”. 2007.13309

Zoo code information

Internal code ID: galois_bch

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

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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Permanent link:
https://errorcorrectionzoo.org/c/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

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qudits_galois/galois_bch.yml.