Generalized Cyclotomic Sequences of Order Four Over Z_(pq) and Their Autocorrelation Values

In this paper, we first introduce two kinds of generalized cyclotomic sequences of order four over Zpq, and then calculate the autocorrelation values of these sequences. The periodic autocorrelation function of the first kind of sequences is seven-valued and the second kind of sequences five-valued. If the two primes p, q are chosen properly, the autocorrelation values of the first kind of sequence can be reduced to six-value or five-value if (p - 1)(q - 1)/16 is even and five-value if (p - 1)(q - 1)/16 is odd, respectively. If q - p = 4, the second kind of sequence has the optimal autocorrelation.