Linear complexity of quaternary sequences over Z4 based on Ding-Helleseth generalized cyclotomic classes

A family of quaternary sequences over Z4 is defined based on the Ding-Helleseth generalized cyclotomic classes modulo pq for two distinct odd primes p and q. The linear complexity is determined by computing the defining polynomial of the sequences, which is in fact connected with the discrete Fourier transform of the sequences. The results show that the sequences possess large linear complexity and are good sequences from the viewpoint of cryptography.