### Arithmetic Cross-correlations of FCSR Sequences

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

Andrew Klapper, 779A Anderson Hall, Dept. of Computer Science,
University of Kentucky, Lexington, KY, 40506-0046, klapper at cs.uky.edu.
www.cs.uky.edu/~klapper/andy.html

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