Extension of the notion of collision and avalanche effect to sequences of k symbols

Abstract

In recent papers [14], [15] I studied collision and avalanche effect in families of finite pseudorandom binary sequences. Motivated by applications, Mauduit and Sarkozy in [13] generalized and extended this theory from the binary case to k-ary sequences, i.e., to k symbols. They constructed a large family of k-ary sequences with strong pseudorandom properties. In this paper our goal is to extend the study of the pseudorandom properties mentioned above to k-ary sequences. The aim of this paper is twofold. First we will extend the definitions of collision and avalanche effect to k-ary sequences, and then we will study these related properties in a large family of pseudorandom k-ary sequences with “small” pseudorandom measures.