d-Form Sequences: Families of Sequences with Low Correlation Values and Large Linear Spans

IEEE Transactions on Information Theory 41 (1995) 423-431.

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

Abstract Large families of binary sequences with low correlation values and large linear span are critical for spread spectrum communication systems. In this paper we describe a method for constructing such families from families of homogeneous functions over finite fields, satisfying certain properties. We then use this general method to construct specific families of sequences with optimal correlations and exponentially better linear span than No sequences.

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