Pseudo-cyclic codes and the construction of quantum MDS codes

Shuxing Li; Maosheng Xiong; Gennian Ge

doi:10.1109/TIT.2016.2535180

Pseudo-cyclic codes and the construction of quantum MDS codes

Shuxing Li, Maosheng Xiong, Gennian Ge

Department of Mathematics

Research output: Contribution to journal › Journal Article › peer-review

39 Citations (Scopus)

Abstract

Constacyclic codes which generalize the classical cyclic codes have played important roles in recent constructions of many new quantum maximum distance separable (MDS) codes. However, the mathematical mechanism may not have been fully understood. In this paper, we use pseudo-cyclic codes, which is a further generalization of constacyclic codes, to construct the quantum MDS codes. We can not only provide a unified explanation of many previous constructions, but also produce some new quantum MDS codes.

Original language	English
Article number	7420695
Pages (from-to)	1703-1710
Number of pages	8
Journal	IEEE Transactions on Information Theory
Volume	62
Issue number	4
DOIs	https://doi.org/10.1109/TIT.2016.2535180
Publication status	Published - Apr 2016

Bibliographical note

Publisher Copyright:
© 2016 IEEE.

Keywords

Hermitian construction
pseudo-cyclic codes
quantum MDS codes

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10.1109/TIT.2016.2535180

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AU - Xiong, Maosheng

AU - Ge, Gennian

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N2 - Constacyclic codes which generalize the classical cyclic codes have played important roles in recent constructions of many new quantum maximum distance separable (MDS) codes. However, the mathematical mechanism may not have been fully understood. In this paper, we use pseudo-cyclic codes, which is a further generalization of constacyclic codes, to construct the quantum MDS codes. We can not only provide a unified explanation of many previous constructions, but also produce some new quantum MDS codes.

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KW - pseudo-cyclic codes

KW - quantum MDS codes

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Pseudo-cyclic codes and the construction of quantum MDS codes

Abstract

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Keywords

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