Combinatorial construction of linear quantum codes from quaternary BCH codes

Ruihu Li; Zongben Xu

doi:10.1142/S0219749909005687

Combinatorial construction of linear quantum codes from quaternary BCH codes

Ruihu Li
, Zongben Xu

数学与统计学院

Xi'an Jiaotong University

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

摘要

Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes. But for given restricted length n, good quantum BCH codes are very sparse. In this paper, by puncturing and pasting check matrices of Hermitian dual containing BCH codes over the quaternary field, we construct many linear quantum codes with good parameters, and some of them have parameters exceeding the finite Gilbert-Varshamov bound for stabilizer quantum codes.

源语言	英语
页（从-至）	1039-1046
页数	8
期刊	International Journal of Quantum Information
卷	7
期	5
DOI	https://doi.org/10.1142/S0219749909005687
出版状态	已出版 - 2009

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N2 - Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes. But for given restricted length n, good quantum BCH codes are very sparse. In this paper, by puncturing and pasting check matrices of Hermitian dual containing BCH codes over the quaternary field, we construct many linear quantum codes with good parameters, and some of them have parameters exceeding the finite Gilbert-Varshamov bound for stabilizer quantum codes.

AB - Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes. But for given restricted length n, good quantum BCH codes are very sparse. In this paper, by puncturing and pasting check matrices of Hermitian dual containing BCH codes over the quaternary field, we construct many linear quantum codes with good parameters, and some of them have parameters exceeding the finite Gilbert-Varshamov bound for stabilizer quantum codes.

KW - Linear quantum error correcting code

KW - Quaternary code

KW - Self-orthogonal code

UR - https://www.scopus.com/pages/publications/69349087476

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Combinatorial construction of linear quantum codes from quaternary BCH codes

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