Galois-qudit GRS code[1,2] 

Description

True \(q\)-Galois-qudit stabilizer code constructed from GRS codes via either the Hermitian construction [24] or the Galois-qudit CSS construction [1,5].

Rate

Concatenations of quantum GRS codes and random stabilizer codes can achieve the quantum GV bound [6].

Parent

Child

Cousins

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
[6]
Y. Ouyang, “Concatenated Quantum Codes Can Attain the Quantum Gilbert–Varshamov Bound”, IEEE Transactions on Information Theory 60, 3117 (2014) arXiv:1004.1127 DOI
[7]
M. Marcolli, “Holographic Codes on Bruhat--Tits buildings and Drinfeld Symmetric Spaces”, (2018) arXiv:1801.09623
[8]
M. Heydeman et al., “Nonarchimedean Holographic Entropy from Networks of Perfect Tensors”, (2018) arXiv:1812.04057
[9]
K. Guenda, S. Jitman, and T. A. Gulliver, “Constructions of Good Entanglement-Assisted Quantum Error Correcting Codes”, (2016) arXiv:1606.00134
[10]
P. J. Nadkarni and S. S. Garani, “Entanglement-assisted Reed–Solomon codes over qudits: theory and architecture”, Quantum Information Processing 20, (2021) DOI
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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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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/edit/main/codes/quantum/qudits_galois/stabilizer/evaluation/rs/galois_grs.yml.