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Linear codes with few weights from weakly regular bent functions based on a generic construction

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Abstract

We contribute to the knowledge of linear codes with few weights from special polynomials and functions. Substantial efforts (especially due to C. Ding) have been directed towards their study in the past few years. Such codes have several applications in secret sharing, authentication codes, association schemes and strongly regular graphs. Based on a generic construction of linear codes from mappings and by employing weakly regular bent functions, we provide a new class of linear p-ary codes with three weights given with its weight distribution. The class of codes presented in this paper is different from those known in literature.

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Acknowledgments

The author would like to thank Prof. Cunsheng Ding for his valuable and constructive comments on a preliminary version of this paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Paris VIII, University of Paris XIII, CNRS, UMR 7539 LAGA and Telecom ParisTech, Paris, France

    Sihem Mesnager

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  1. Sihem Mesnager
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Correspondence to Sihem Mesnager.

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Mesnager, S. Linear codes with few weights from weakly regular bent functions based on a generic construction. Cryptogr. Commun. 9, 71–84 (2017). https://doi.org/10.1007/s12095-016-0186-5

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  • DOI: https://doi.org/10.1007/s12095-016-0186-5

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