Abstract
Quadratic functions Fp,n defined from Fpn to Fp with coefficients in Fp, have been studied in several papers. In 2014, Meidl, Roy and Topuzoglu gave three methods for enumeration of such functions with prescribed Walsh spectrum. They obtained the generating functions for the counting functions when n is odd and relatively prime to p, or when n = 2m for odd m and p = 2. In 2015, Cesmelioglu and Meidl presented the generating functions when n is even and relatively prime to p for odd p. In this paper, we extend previous results and propose the generic generating functions for the counting functions for arbitrary n and p. In particular, the respective numbers of bent functions and semi-bent functions are determined.