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Complete weight enumerators of a family of three-weight linear codes

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Abstract

Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime p, we present the explicit complete weight enumerator of a family of p-ary linear codes constructed with defining set. The weight enumerator is an immediate result of the complete weight enumerator, which shows that the codes proposed in this paper are three-weight linear codes. Additionally, all nonzero codewords are minimal and thus they are suitable for secret sharing.

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Acknowledgments

The authors are very grateful to the editor and the anonymous reviewers for their helpful comments and 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). This work is also partially supported by the NSFC (Grant No. 61472457) and 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

  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 Shudi Yang.

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Communicated by C. Ding.

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Yang, S., Yao, ZA. Complete weight enumerators of a family of three-weight linear codes. Des. Codes Cryptogr. 82, 663–674 (2017). https://doi.org/10.1007/s10623-016-0191-x

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