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Complete weight distributions of two classes of cyclic codes

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Abstract

Complete weight distribution can be used to study authentication codes and the Walsh transform of monomial functions over finite fields. Also, the Hamming weight distribution of a code can be obtained from its complete weight distribution. In this paper, we investigate the complete weight distributions of two classes of cyclic codes. We explicitly present the complete weight enumerators of the cyclic codes. Particularly, we partly solve an open problem proposed in Luo and Feng (IEEE Trans. Inf. Theory 54(12), 5345–5353 (2008)).

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Acknowledgments

The authors are very grateful to the reviewers and the Editor, Prof. Tor Helleseth, for their detailed comments and suggestions that much improved the quality of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, People’s Republic of China

    Ziling Heng & Qin Yue

  2. State Key Laboratory of Cryptology, P. O. Box 5159, Beijing, 100878, People’s Republic of China

    Qin Yue

Authors
  1. Ziling Heng
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  2. Qin Yue
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Corresponding authors

Correspondence to Ziling Heng or Qin Yue.

Additional information

The paper is supported by NNSF of China (No. 11171150); Fundamental Research Funds for the Central Universities (No. NZ2015102); Funding of Jiangsu Innovation Program for Graduate Education (Fundamental Research Funds for the Central Universities; No. KYZZ15-0086); Foundation of Science and Technology on Information Assurance Laboratory (No. KJ-15-009).

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Heng, Z., Yue, Q. Complete weight distributions of two classes of cyclic codes. Cryptogr. Commun. 9, 323–343 (2017). https://doi.org/10.1007/s12095-015-0177-y

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  • DOI: https://doi.org/10.1007/s12095-015-0177-y

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