Galois-qudit GRS code[1][2]

Description

True \(q\)-Galois-qudit stabilizer code constructed from generalized Reed-Solomon (GRS) codes via either the Hermitian construction [2][3][4] or the Galois-qudit CSS construction [1].

Parent

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

Child

Cousins

References

[1]
Dorit Aharonov and Michael Ben-Or, “Fault-Tolerant Quantum Computation With Constant Error Rate”. quant-ph/9906129
[2]
Lingfei Jin and Chaoping Xing, “A Construction of New Quantum MDS Codes”. 1311.3009
[3]
X. Liu, L. Yu, and H. Liu, “New quantum codes from Hermitian dual-containing codes”, International Journal of Quantum Information 17, 1950006 (2019). DOI
[4]
L. Jin et al., “Application of Classical Hermitian Self-Orthogonal MDS Codes to Quantum MDS Codes”, IEEE Transactions on Information Theory 56, 4735 (2010). DOI

Zoo code information

Internal code ID: galois_grs

Your contribution is welcome!

on github.com (edit & pull request)

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Zoo Code ID: galois_grs

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

Cite as:

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

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