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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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