Cross-Correlations of Geometric Sequences in Characteristic Two

Designs, Codes, and Cryptography 3 (1993) 347-377.

Andrew Klapper, 779A Anderson Hall, Dept. of Computer Science, University of Kentucky, Lexington, KY, 40506-0046, klapper at

Abstract Cross-correlation functions are determined for a large class of geometric sequences based on m-sequences in characteristic two. These sequences are shown to have low cross-correlation values in certain cases. They are also shown to have significantly higher linear complexities than previously studied geometric sequences. These results show that geometric sequences are candidates for use in spread-spectrum communications systems in which cryptographic security is a factor.

Index Terms -- Binary sequence, geometric sequence, cross-correlation, linear complexity, Galois field.