On vectorial functions with maximal number of bent components

01/07/2023

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by   Xianhong Xie, et al.

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We study vectorial functions with maximal number of bent components in this paper. We first give a construction of such functions from known ones, thus obtain two new classes from the Niho class and the Maiorana-McFarland class. Our construction gives a partial answer to an open problem proposed by Pott et al., and also solves an open problem proposed by Mesnager. We then show that the vectorial function F: _2^2m→_2^2m, x↦ x^2^m+1+x^2^i+1 has maximal number of bent components if and only if i=0.