Three new infinite families of bent functions
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Bent functions are maximally nonlinear Boolean functions with an even number of variables. They are closely related to some interesting combinatorial objects and also have important applications in coding, cryptography and sequence design. In this paper, we firstly give a necessary and sufficient condition for a type of Boolean functions, which obtained by adding the product of finitely many linear functions to given bent functions, to be bent. In the case that these known bent functions are chosen to be Kasami functions, Gold-like functions and functions with Niho exponents, respectively, three new explicit infinite families of bent functions are obtained. Computer experiments show that the proposed familes also contain such bent functions attaining optimal algebraic degree.
Keywordsbent function Hadamard matrix Kasami function Gold-like function Niho exponent
This work was supported by National Natural Science Foundation of China (Grant Nos. 61502482, 61379139, 11526215), National Key Research Program of China (Grant No. 2016YFB0800401), and “Strategic Priority Research Program” of Chinese Academy of Sciences (Grant No. XDA06010701).
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