Quadratic Bent and Semi-bent Functions over Finite Fields of Odd Characteristic

Let n=me and p be an odd prime. Let F_p be a finite field and F_pⁿ be its nth field extension. By some polynomial GCD computations, this paper characterize the bentness and semi-bentness of two classes of p-ary quadratic functions from F_pⁿ to F_p with coefficients in F_p^e . Moreover, the enumeration formulas of constructed bent functions are obtained for some special cases of m. The results generalize some previous related work.