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COMBINATORIAL CONSTRUCTION OF LINEAR QUANTUM CODES FROM QUATERNARY BCH CODES

RUIHU LI

College of Science, Xi'an Jiaotong University, Shaanxi 710049, People's Republic of China

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and

ZONGBEN XU

Institute for Information and System Sciences, Xi'an Jiaotong University, Shaanxi 710049, People's Republic of China

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https://doi.org/10.1142/S0219749909005687Cited by:4 (Source: Crossref)

Abstract

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.

Keywords:

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