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Optimal p-ary cyclic codes with minimum distance four from monomials

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Abstract

For any odd prime p≥5, some optimal p-ary cyclic codes with parameters [p m−1,p m−2m−2,4] are presented by using perfect nonlinear monomials and the inverse function over \(\mathbb {F}_{p^{m}}\). In addition, almost perfect nonlinear monomials, and other monomials over \(\mathbb {F}_{5^{m}}\) are used to construct optimal quinary cyclic codes with parameters [5m−1,5m−2m−2,4].

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Acknowledgments

The authors are grateful to the anonymous referees for their helpful comments and suggestions. This research is supported by NNSF Grant of China (11371011, 61403157 and 61572027) and Natural Science Foundation for the Higher Education Institutions of Anhui Province of China (KJ2015A256).

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Guangkui Xu, Xiwang Cao & Shanding Xu

  2. Department of Applied Mathematics, Huainan Normal University, Huainan, 232038, China

    Guangkui Xu

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

    Xiwang Cao

  4. Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing, 210016, China

    Shanding Xu

Authors
  1. Guangkui Xu
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  2. Xiwang Cao
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  3. Shanding Xu
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Correspondence to Guangkui Xu or Xiwang Cao.

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Xu, G., Cao, X. & Xu, S. Optimal p-ary cyclic codes with minimum distance four from monomials. Cryptogr. Commun. 8, 541–554 (2016). https://doi.org/10.1007/s12095-015-0159-0

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  • DOI: https://doi.org/10.1007/s12095-015-0159-0

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