| Abstrakt: |
In 2017, Tang et al. have introduced a generic construction for bent functions of the form f (x) = g (x) + h (x) , where g is a bent function satisfying some conditions and h is a Boolean function. Recently, Zheng et al. (Discret Math 344:112473, 2021) generalized this result to construct large classes of bent vectorial Boolean functions from known ones in the form F (x) = G (x) + h (X) , where G is a vectorial bent and h is a Boolean function. In this paper, we further generalize this construction to obtain vectorial bent functions of the form F (x) = G (x) + H (X) , where H is also a vectorial Boolean function. This allows us to construct new infinite families of vectorial bent functions, EA-inequivalent to G, which was used in the construction. Most notably, specifying H (x) = h (T r 1 n (u 1 x) , ... , T r 1 n (u t x)) , the function h : F 2 t → F 2 t can be chosen arbitrarily, which gives a relatively large class of different functions for a fixed function G. We also propose a method of constructing vectorial (n, n)-functions having maximal number of bent components. [ABSTRACT FROM AUTHOR] |
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