International Association
for Cryptologic Research

In this paper, we generalize some existing results on Boolean

functions to the $q$-ary functions defined over $\\BBZ_q$, where

$q\\geq 2$ is an integer, and obtain some new characterization of

$q$-ary functions based on spectral analysis. We provide a

relationship between Walsh-Hadamard spectra of two $p$-ary functions

$f$ and $g$ (for $p$ a prime) and their derivative $D_{f, g}$. We

provide a relationship between the Walsh-Hadamard spectra and the

decompositions of any two $p$-ary functions. Further, we investigate

a relationship between the Walsh-Hadamard spectra and the

autocorrelation of any two $q$-ary functions.