Large Families of Sequences with Near Optimal Correlations and Large Linear Span

IEEE Transactions on Information Theory 42 (1996) 1241-1248.

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

Abstract In order to build spread spectrum communication systems based on the CDMA paradigm, it is necessary to have large families of binary sequences with low pairwise correlation values. For these systems to have resistance to certain cryptanalytic attacks and resistance to jamming, the sequences must have large linear span. In this paper we describe certain families of sequences that have these desirable properties. The sequences are based on families of quadratic forms over finite fields.

Index Terms -- Cross-correlation, autocorrelation, linear span, binary sequences, families of sequences, No sequences, spread spectrum, CDMA, finite fields, quadratic forms.