Characterization and Construction of Generalized Bent Functions with Flexible Coefficients

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  • YANG Zhiyao
    Fujian Provincial Key Laboratory of Network Security and Cryptology, Fujian Normal University
  • KE Pinhui
    School of Mathematics and Statistics, Fujian Normal University
  • CHEN Zhixiong
    Provincial Key Laboratory of Applied Mathematics, Putian University

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<p>In 2017, Tang et al. provided a complete characterization of generalized bent functions from ℤ2n to ℤq(q = 2m) in terms of their component functions (IEEE Trans. Inf. Theory. vol.63, no.7, pp.4668-4674). In this letter, for a general even q, we aim to provide some characterizations and more constructions of generalized bent functions with flexible coefficients. Firstly, we present some sufficient conditions for a generalized Boolean function with at most three terms to be gbent. Based on these results, we give a positive answer to a remaining question proposed by Hodžić in 2015. We also prove that the sufficient conditions are also necessary in some special cases. However, these sufficient conditions whether they are also necessary, in general, is left as an open problem. Secondly, from a uniform point of view, we provide a secondary construction of gbent function, which includes several known constructions as special cases.</p>

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