New M-Ary Sequence Families With Low Correlation and Large Size

Abstract

In this paper, we construct four M-ary sequence families from a power residue sequence of odd prime period p and its constant multiple sequences using the shift-and-add method, when M is a divisor of p - 1. We show that the maximum correlation values of the proposed sequence families are upper-bounded by 2 root p+5 or 3 root p+4. In addition, we prove that the linear complexity of each sequence in the proposed families is either p-1 or p-p-1/M-1. We also construct an M-ary sequence family from Sidel'nikov sequences of period p(m) - 1 by applying the same method, when M is a divisor of p(m) - 1. The proposed sequence family (F-s) over tilde has larger size than the known M-ary Sidel'nikov sequence families, whereas they all have the same upper bound on the maximum correlation.