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Five classes of optimal two-weight linear codes

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Abstract

Linear codes with few weights have applications in secret sharing, authentication codes, association schemes, data storage systems, strongly regular graphs and some other fields. Two-weight linear codes are particularly interesting since they are closely related to finite geometry, combinatorial designs, graph theory. In this paper, we propose five classes of two-Lee-weight codes over the ring \(\mathbb {F}_{q}+u\mathbb {F}_{q}\). By the Gray map, we obtain five classes of linear codes with two weights over \(\mathbb {F}_{q}\) and these linear codes are optimal with respect to the Griesmer bound. As applications, we can employ these linear codes to construct secret sharing schemes with nice access structures.

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Acknowledgments

We are grateful to the anonymous referees and the editor for useful comments and suggestions that improved the presentation and quality of this paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Gaojun Luo & Xiwang Cao

  2. State Key Laboratory of Information Security Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Xiwang Cao

Authors
  1. Gaojun Luo
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  2. Xiwang Cao
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Corresponding author

Correspondence to Gaojun Luo.

Additional information

This work was supported by the National Natural Science Foundations of China (Grant Nos. 11371011, 11771007 and 61572027)

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Luo, G., Cao, X. Five classes of optimal two-weight linear codes. Cryptogr. Commun. 10, 1119–1135 (2018). https://doi.org/10.1007/s12095-017-0272-3

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  • DOI: https://doi.org/10.1007/s12095-017-0272-3

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