Arithmetic Cross-correlations of FCSR Sequences

IEEE Transactions on Information Theory 43 (1997) 1342-1346.

Andrew Klapper, 779A Anderson Hall, Dept. of Computer Science, University of Kentucky, Lexington, KY, 40506-0046, klapper at
Mark Goresky, Institute for Advanced Study

Abstract An arithmetic version of the cross-correlation of two sequences is defined, generalizing Mandelbaum's arithmetic autocorrelations. Large families of sequences are constructed with ideal (vanishing) arithmetic cross-correlations. These sequences are decimations of the 2-adic expansions of rational numbers $p/q$ such that 2 is a primitive root modulo $q$.

Index Terms -- Cross-correlations, 2-Adic Numbers, Binary Sequences, FCSR Sequences