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Binary linear codes with two or three weights from niho exponents

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Abstract

Linear codes with few weights have applications in secret sharing, authentication codes, association schemes, date storage systems, strongly regular graphs and some other fields. In this paper, we present several classes of binary linear codes with two or three weights and study their weight distributions. Two classes of strongly regular graphs are constructed from binary linear codes with two weights. Numerical results show that some of the obtained codes are either optimal or near optimal with respect to certain bounds on linear codes.

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Acknowledgments

We are grateful to the two anonymous referees and the editor for useful comments and suggestions that improved the presentation and quality of this paper. Particular thanks to one of the reviewers for pointing out the connection set of the Cayley graphs in Theorem 6.

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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, Shanding Xu & Jiafu Mi

  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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  3. Shanding Xu
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  4. Jiafu Mi
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Corresponding authors

Correspondence to Gaojun Luo or Xiwang Cao.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 11371011 and 61572027), the Funding of Jiangsu Innovation Program for Graduate Education (Grant No. KYZZ15 _0090).

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Luo, G., Cao, X., Xu, S. et al. Binary linear codes with two or three weights from niho exponents. Cryptogr. Commun. 10, 301–318 (2018). https://doi.org/10.1007/s12095-017-0220-2

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  • DOI: https://doi.org/10.1007/s12095-017-0220-2

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