Periodicity and Correlation Properties of $d$-FCSR Sequences

Designs, Codes, and Cryptography, 33 (2004) 123-148.

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

Abstract Statistical properties are studied for certain sequences based on the arithmetic of totally ramified extensions of the rational numbers. A simplified exponential representation is found. The arithmetic cross-correlations are shown in some cases to vanish identically. Bounds on the distribution of subsequences are found.

Index Terms -- Cross-correlations, 2-Adic Numbers, Binary Sequences, Number Field.