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Let $n$ be an even positive integer, and $m<n$ be one of its positivedivisors. In this paper, inspired by a nice work of Tang et al. on constructinglarge classes of bent functions from known bent functions [27, IEEE TIT,63(10): 6149-6157, 2017], we consider the construction of vectorial bent andvectorial 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 functionover $\mathbb{F}_{2^{n}}$. We find an efficient generic method to constructvectorial bent and vectorial plateaued functions of this form by establishing alink between the condition on the second-order derivatives and the keycondition given by [27]. This allows us to provide (at least) three newinfinite families of vectorial bent functions with high algebraic degrees. Newvectorial plateaued $(n,m+t)$-functions are also obtained ($t\geq 0$ dependingon $n$ can be taken as a very large number), two classes of which have themaximal number of bent components.

Constructing vectorial bent functions via second-order derivatives