Pseudo-randomness of certain sequences of k symbols with length pq

Authors:
Zhi-Xiong Chen;Xiao-Ni Du;Chen-Huang Wu
Affiliations:
Department of Mathematics, Putian University, Putian, China and State Key Lab. of ISN, Xidian University, Xi'an, China;State Key Lab. of ISN, Xidian University, Xi'an, China and College of Mathematics and Information Science, Northwest Normal University, Lanzhou, China;Department of Mathematics, Putian University, Putian, China
Venue:
Journal of Computer Science and Technology
Year:
2011

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Abstract

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.