Generalized M-ary Related-Prime Sequences with Low Correlation

In this paper we introduce new M-ary sequences of length pq, called generalized M-ary related-prime sequences, where p and q are distinct odd primes, and M is a common divisor of p - 1 and q - 1. We show that their out-of-phase autocorrelation values are upper bounded by the maximum between q - p + 1 and 5. We also construct a family of generalized M-ary related-prime sequences and show that the maximum correlation of the proposed sequence family is upper bounded by p + q -1.