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  • 1 Department of Computer Algebra, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary
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Abstract  

In recent papers [14], [15] I studied collision and avalanche effect in families of finite pseudorandom binary sequences. Motivated by applications, Mauduit and Sárközy 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.