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A class of three-weight linear codes over finite fields of odd characteristic

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Applied in communication, data storage system, secret sharing schemes, authentication codes and association schemes, linear codes attract much attention. In this paper, a class of three-weight linear codes is obtained by the defining sets over finite fields of odd characteristic. The parameters and weight distributions of linear codes are determined by the additive characters, multiplicative characters and Gauss sums. Further, most of linear codes obtained are minimal, which can be used to construct secret sharing schemes.

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Acknowledgements

The authors are very grateful to the anonymous reviewers and the Editor, for their valuable comments and suggestions that improved the presentation and quality of this paper. This paper was supported by Zhejiang provincial Natural Science Foundation of China (No. LY21A010013).

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Authors and Affiliations

  1. School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China

    Bingbing Duan, Guangguo Han & Yanfeng Qi

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  1. Bingbing Duan
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  2. Guangguo Han
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  3. Yanfeng Qi
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Correspondence to Yanfeng Qi.

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Duan, B., Han, G. & Qi, Y. A class of three-weight linear codes over finite fields of odd characteristic. AAECC 35, 359–375 (2024). https://doi.org/10.1007/s00200-022-00554-7

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  • DOI: https://doi.org/10.1007/s00200-022-00554-7

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