Pseudo-Randomness of Certain Sequences of <Emphasis Type="Italic">k</Emphasis> Symbols with Length <Emphasis Type="Italic">pq</Emphasis>

The theory of finite pseudo-random binary sequences was built by C. Mauduit and A. Sárközy and later extended to sequences of k symbols (or k-ary sequences). Certain constructions of pseudo-random sequences of k symbols were presented over finite fields in the literature. In this paper, two families of sequences of k symbols are constructed by using the integers modulo pq for distinct odd primes p and q. The upper bounds on the well-distribution measure and the correlation measure of the families sequences are presented in terms of certain character sums over modulo pq residue class rings. And low bounds on the linear complexity profile are also estimated.