Discovery of Multiple-Valued Bent Functions in Galois Field and Reed-Muller-Fourier Domains

Abstract

Multiple-valued bent functions are a special class of functions which have the highest possible nonlinearity. As the multiple-valued order and number of variables of the functions increases, the probability of discovery of bent functions extremely decreases. Thus, this paper presents a method for random discovery of bent functions in Galois Field and Reed-Muller-Fourier domains. Experimental results are included in order to verify that the proposed computational method reduces the time needed for discovery of random bent ternary and quaternary functions and, in this way, might extend the possibilities for their practical application.