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EA MDS code[13]

Description

EA Galois-qudit code whose parameters make the EAQECC Singleton bound (a.k.a. qubit-ebit Singleton bound) [3; Thm. 6] become an equality.

The original EAQECC Singleton bound [1,4] was shown to be erroneous [5] and corrected in Ref. [3].

Cousins

References

[1]
T. Brun, I. Devetak, and M.-H. Hsieh, “Correcting Quantum Errors with Entanglement”, Science 314, 436 (2006) arXiv:quant-ph/0610092 DOI
[2]
C.-Y. Lai and T. A. Brun, “Entanglement increases the error-correcting ability of quantum error-correcting codes”, Physical Review A 88, (2013) arXiv:1008.2598 DOI
[3]
M. Grassl, F. Huber, and A. Winter, “Entropic Proofs of Singleton Bounds for Quantum Error-Correcting Codes”, IEEE Transactions on Information Theory 68, 3942 (2022) arXiv:2010.07902 DOI
[4]
T. A. Brun, I. Devetak, and M.-H. Hsieh, “Catalytic Quantum Error Correction”, IEEE Transactions on Information Theory 60, 3073 (2014) arXiv:quant-ph/0608027 DOI
[5]
M. Grassl, “Entanglement-assisted quantum communication beating the quantum Singleton bound”, Physical Review A 103, (2021) arXiv:2007.01249 DOI
[6]
J. Fan, H. Chen, and J. Xu, “Constructions of q-ary entanglement-assisted quantum MDS codes with minimum distance greater than q + 1”, (2016) arXiv:1602.02235
[7]
N. R. Dash, S. Dutta, R. Srikanth, and S. Banerjee, “Bounds on concatenated entanglement-assisted quantum error-correcting codes”, (2024) arXiv:2412.16082
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Cite as:

“EA MDS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/ea_mds

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits_galois/ea_stabilizer/ea_mds.yml.