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A class of negacyclic BCH codes and its application to quantum codes

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Abstract

In this paper, we study negacyclic BCH codes over \(\mathbb {F}_{q}\) of length \(n=(q^{2m}-1)/(q-1)\), where q is an odd prime power and m is a positive integer. In particular, the dimension, the minimum distance and the weight distribution of some negacyclic BCH codes over \(\mathbb {F}_{q}\) of length \(n=(q^{2m}-1)/(q-1)\) are determined. Two classes of negacyclic BCH codes meeting the Griesmer bound are obtained. As an application, we construct quantum codes with good parameters from this class of negacyclic BCH codes.

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Acknowledgements

The authors would like to thank the anonymous referees who gave many helpful comments and suggestions to greatly improve the presentation of the paper. The research was supported in part by the National Natural Science Foundation of China under Grant Nos. 61772168, 61572168 and 11501156.

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Authors and Affiliations

  1. School of Mathematics, Hefei University of Technology, Hefei, 230009, Anhui, China

    Shixin Zhu, Zhonghua Sun & Ping Li

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  1. Shixin Zhu
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  2. Zhonghua Sun
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  3. Ping Li
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Correspondence to Zhonghua Sun.

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Communicated by A. Winterhof.

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Zhu, S., Sun, Z. & Li, P. A class of negacyclic BCH codes and its application to quantum codes. Des. Codes Cryptogr. 86, 2139–2165 (2018). https://doi.org/10.1007/s10623-017-0441-6

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  • DOI: https://doi.org/10.1007/s10623-017-0441-6

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