Constructing vectorial bent functions via second-order derivatives
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Let n be an even positive integer, and m<n be one of its positive divisors. In this paper, inspired by a nice work of Tang et al. on constructing large classes of bent functions from known bent functions [27, IEEE TIT, 63(10): 6149-6157, 2017], we consider the construction of vectorial bent and vectorial plateaued (n,m)-functions of the form H(x)=G(x)+g(x), where G(x) is a vectorial bent (n,m)-function, and g(x) is a Boolean function over F_2^n. We find an efficient generic method to construct vectorial bent and vectorial plateaued functions of this form by establishing a link between the condition on the second-order derivatives and the key condition given by [27]. This allows us to provide (at least) three new infinite families of vectorial bent functions with high algebraic degrees. New vectorial plateaued (n,m+t)-functions are also obtained (t≥ 0 depending on n can be taken as a very large number), two classes of which have the maximal number of bent components.
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