Some Notes on Generalized Cyclotomic Sequences of Length pq

We review the constructions of two main kinds of generalized cyclotomic binary sequences with length pq (the product with two distinct primes). One is the White-generalized cyclotomic sequences, the other is the Ding-Helleseth(DH, for short)-generalized cyclotomic sequences. We present some new pseudo-random properties of DH-generalized cyclotomic sequences using the theory of character sums instead of the theory of cyclotomy, which is a conventional method for investigating generalized cyclotomic sequences. Electronic supplementary material The online version of this article (doi: ) contains supplementary material, which is available to authorized users. This work was supported in part by the Open Funds of Key Lab of Fujian Province University Network Security and Cryptology (Grant No. 07B005), the Funds of the Education Department of Fujian Province (Grant No. JA07164) and the Natural Science Foundation of Fujian Province of China (Grant No. 2007F3086).