Paper 2013/617

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

Brajesh Kumar Singh

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 $f\in {\text{cB}}_{n,q}$ in terms of ${\sigma }_{f_{\ell }}^{\prime }$s of the restricted functions on ${\text{BBZ}}_{n-1}^q$, and construct a class of $q$-ary bent functions from $1$-plateaued functions having dijoint Walsh spectra.