p-valued Maiorana-McFarland Functions Structure of Their Reed-Muller Spectra

Abstract

p-valued Maiorana-McFarland bent functions exist, as in the binary case, only for an even number of variables and they are normally associated to their Discrete Fourier spectra in order to specify their bentness through the flatness of the spectra. In this paper, a closely related, but different approach is considered. Structural properties of the Reed-Muller spectra of p-valued Maiorana-McFarland bent functions are studied when p > 2 is a prime. It is shown that the Reed-Muller spectra of p-valued Maiorana-McFarland bent functions have a regressive structure, parameterized by p and k, where n = 2k denotes the even number of variables.