Constructing vectorial bent functions via second-order derivatives

Let n be an even positive integer, and m<n one of its divisors. In this paper, inspired by the work Tang et al. (2017) [23] on constructing large classes bent functions from known ones, we consider construction vectorial plateaued (n,m)-functions form H(x)=G(x)+g(x), where G is a (n,m)-function, g Boolean function. We find efficient generic method to construct such kind (plateaued) establishing link between bentness (plateaudness) H second-order derivatives g. This allows us provide (at least) three new infinite families with high algebraic degrees. New (n,m+t)-functions are also obtained (t≥0 depending can numbers), two which have maximal number components.