A Class of New Quadratic Vectorial Bent Functions

A class of quadratic vectorial bent functions having the form F (x)=Tr_mⁿ (ax^2s1 +1) + Tr₁ⁿ (bx^2s2 +1) is investigated, where n, m, s₁, s₂ are positive integers and the coefficients a, b belong to the finite field F_2ⁿ. Through some discussions on the permutation property of certain linearized polynomials over F_2ⁿ, several classes of quadratic vectorial bent functions are presented for special cases of n, and it is also verified by computer that some vectorial bent functions proposed are extended affine inequivalent to all known quadratic vectorial bent functions.