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

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 2radicp +5 or 3radicp +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 tilde _s has larger size than the known M-ary Sidel´nikov sequence families, whereas they all have the same upper bound on the maximum correlation.