Boolean functions with six-valued Walsh spectra and their application

Abstract

Boolean functions play an important role in coding theory and symmetric cryptography. In this paper, three classes of Boolean functions with six-valued Walsh spectra are presented and their Walsh spectrum distributions are determined. They are derived from three classes of bent functions by complementing the values of the functions at three different points, where the bent functions are the Maiorana-McFarland types, Dillon $\mathcal {PS}_{ap}$ types and the monomial form $T{r^{n}_{1}}(\lambda x^{r(2^{m}-1)})$ , respectively. As an application, we construct some classes of binary linear codes and it turns out that these codes can be used in secret sharing schemes with interesting access structure.