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A class of three-weight linear codes and their complete weight enumerators

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Abstract

Recently, linear codes constructed from defining sets have been investigated extensively and they have many applications. In this paper, for an odd prime p, we propose a class of p-ary linear codes by choosing a proper defining set. Their weight enumerators and complete weight enumerators are presented explicitly. Our results show that they are linear codes with three weights and suitable for the constructions of authentication codes and secret sharing schemes.

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Acknowledgments

The authors are very grateful to the editor and the three anonymous referees for their useful comments and important suggestions, which have improved the presentation of this paper. The work of Zheng-An Yao is partially supported by the NSFC (Grant No.11271381), the NSFC (Grant No.11431015) and China 973 Program (Grant No. 2011CB808000). The work of Chang-An Zhao is partially supported by the NSFC (Grant No. 61472457). This work is also partially supported by Guangdong Natural Science Foundation (Grant No. 2014A030313161).

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Authors and Affiliations

  1. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China

    Shudi Yang, Zheng-An Yao & Chang-An Zhao

  2. School of Mathematical Sciences, Qufu Normal University, Shandong, 273165, People’s Republic of China

    Shudi Yang

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  1. Shudi Yang
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  2. Zheng-An Yao
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Correspondence to Chang-An Zhao.

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Yang, S., Yao, ZA. & Zhao, CA. A class of three-weight linear codes and their complete weight enumerators. Cryptogr. Commun. 9, 133–149 (2017). https://doi.org/10.1007/s12095-016-0187-4

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  • DOI: https://doi.org/10.1007/s12095-016-0187-4

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