For any positive integers n= 2 k and m such that m≥ k, in this paper we show that the maximal number of bent components of any (n,m)-function is equal to 2 m- 2 m-k, and for those attaining the equality, their algebraic degree is at most k. It is easily seen that all (n,m)-functions of the form G(x) = (F(x) , 0) , with F(x) being any vectorial bent (n,k)-function, have the maximal number of bent components. Those simple functions G are called trivial in this paper. We show that for a power (n,n)-function, it has the maximal number of bent comp...
