New M-ary Power Residue Sequence Families with Low Correlation

In this paper we construct M-ary sequence families from power residue sequences of odd prime period p and their 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 of size p + M - 2 and (M - 1)² (p - 1)/2 + M - 1 are upper bounded by 2radic(p) + 5 and 3radic(p) + 4, respectively.