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][5].
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
- Generalized RS (GRS) code — Hermitian self-orthogonal GRS codes are used to construct Galois-qudit GRS codes in the Hermitian construction.
- Quantum maximum-distance-separable (MDS) code — Some Galois-qudit GRS codes are quantum MDS [2].
References
- [1]
- D. Aharonov and M. Ben-Or, “Fault-Tolerant Quantum Computation With Constant Error Rate”, (1999) arXiv:quant-ph/9906129
- [2]
- L. Jin and C. Xing, “A Construction of New Quantum MDS Codes”, (2020) arXiv: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
- [5]
- Z. Li, L.-J. Xing, and X.-M. Wang, “Quantum generalized Reed-Solomon codes: Unified framework for quantum maximum-distance-separable codes”, Physical Review A 77, (2008) arXiv:0812.4514 DOI
Page edit log
- Victor V. Albert (2022-07-22) — most recent
Cite as:
“Galois-qudit GRS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/galois_grs