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New Quantum BCH Codes of Length n = r(q2 − 1)

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Abstract

Classical Bose-Chaudhuri-Hocquenghem (BCH) codes over finite fields have studied extensively. The quantum stabilizer codes with good parameters can be constructed using classical BCH codes. In this paper, we study the construction of quantum codes from nonprimitive BCH codes over the finite field \(\mathbb {F}_{q^{2}}\). Taking advantage of Hermitian dual containing BCH codes of length n = r(q2 − 1) over \(\mathbb {F}_{q^{2}}\) where ordn(q2) = 4, we can construct some families of new quantum codes with good parameters.

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Acknowledgments

This study is supported by the National Natural Science Foundation of China (Nos. 61772168, 61972126, 12001002, 62002093) and the Natural Science Foundation of Anhui Province (No. 2008085QA04).

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Authors and Affiliations

  1. School of Mathematics, Hefei University of Technology, Hefei, 230601, Anhui, People’s Republic of China

    Hao Zhang & Shixin Zhu

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  1. Hao Zhang
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  2. Shixin Zhu
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Correspondence to Shixin Zhu.

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Zhang, H., Zhu, S. New Quantum BCH Codes of Length n = r(q2 − 1). Int J Theor Phys 60, 172–184 (2021). https://doi.org/10.1007/s10773-020-04673-0

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  • DOI: https://doi.org/10.1007/s10773-020-04673-0

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