Bent and Permutational Properties of Budaghyan-Carlet Hexanomials

Abstract

The set related to the existence of Budaghyan-Carlet hexanomials is characterized. By investigating the component functions, it is also proved that none of Budaghyan-Carlet hexanomials cannot be turned into a permutation by adding any linearized polynomial. As a byproduct, a class of quadratic bent functions is obtained.