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

摘要

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