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

In this paper, we construct fourM-ary sequence families from apower residue sequenceof odd prime periodpand its constant multiple sequences using the shift-and-add method, whenMis a divisor of$p-1$. We show that the maximum correlation values of the proposed sequence families are upper-bounded by2√p +5or3√p +4. In addition, we prove that the linear complexity of each sequence in the proposed families is either$p\!-\!1$orp\!-\!p-1 M\!-\!1. We also construct anM-ary sequence family fromSidel'nikov sequencesof periodpᵐ-1by applying the same method, whenMis a divisor ofpᵐ-1. The proposed sequence familyFₛhas larger size than the knownM-ary Sidel'nikov sequence families, whereas they all have the same upper bound on the maximum correlation.