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Several classes of Boolean functions with few Walsh transform values

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Abstract

In this paper, several classes of Boolean functions with few Walsh transform values, including bent, semi-bent and five-valued functions, are obtained by adding the product of two or three linear functions to some known bent functions. Numerical results show that the proposed class contains cubic bent functions that are affinely inequivalent to all known quadratic ones.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grants 11371011, 11601177, 61403157, and 61572027), Anhui Provincial Natural Science Foundation (Grant No.1608085QA05), the Foundation for Distinguished Young Talents in Higher Education of Anhui Province of China (Grant No. gxyqZD2016258) and the Funding of Jiangsu Innovation Program for Graduate Education (Grant No. KYZZ\(15_{-}0090\)).

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Authors and Affiliations

  1. School of Mathematical Sciences, 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

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. Several classes of Boolean functions with few Walsh transform values. AAECC 28, 155–176 (2017). https://doi.org/10.1007/s00200-016-0298-3

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  • DOI: https://doi.org/10.1007/s00200-016-0298-3

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