On Quadratic Vectorial Bent Functions in Trace Forms

By permutation behavior of certain linearized polynomials, the bentness of quadratic vectorial bent functions of the form F ( x ) = ∑ i = 1 k − 1Tr m n ( c i x 1 + 2 i t) +Tr m k t ( c k x 1 + 2 k t) is investigated, where n = 2 kt and m | kt with k , t being positive integers. The numerical results show that there exist new quadratic vectorial bent functions obtained up to extended affine equivalence.