A note on constructions of bent functions from involutions.
Sihem Mesnager · 2015
Bent functions are maximally nonlinear Boolean functions. They are important functions introduced by Rothaus and studied firstly by Dillon and next by many re-searchers for four decades. Since the complete classification of bent functions seems elusive, many researchers turn to design constructions of bent functions. In this note, we show that linear involutions (which are an important class of permutations) over finite fields give rise to bent functions in bivariate representations. In particular, we exhibit new constructions of bent functions involving binomial linear involutions whose dual functions are directly obtained without computation. 1