Some results concerning global avalanche characteristics of two $q$-ary functions

Abstract

The global avalanche characteristics criteria was first introduced by Zhou et al. (Inform. Sci. 180(2) (2010) 256-265). This article is concerned with some new bounds on global avalanche characteristics of two $q$-ary functions. Based on the above result we obtain a bound on $\sigma_{f}$ of f \in \cB_{n, q} in terms of $\sigma_{f_{\ell}}\u27$s of the restricted functions on \BBZ_{n-1}^q, and construct a class of $q$-ary bent functions from $1$-plateaued functions having dijoint Walsh spectra