A note on vectorial bent functions

•In this paper, we present three methods to construct vectorial bent Boolean functions.•The first two constructions are based on the monomial bent functions, and the second construction is based on the bent functions given by Dillon.•The problem that the reviewer suggested has been pointed out at the last sentence of the first passage of Section 4, so I did not revise it.

In this paper we give three methods on the constructions of vectorial bent functions from F2n to F2n2, where n is a positive even integer. The first two kinds of functions are based on monomial bent functions. The third kind of functions are based on partial spreads bent functions, and those vectorial bent functions can achieve the largest algebraic degree.