On the Linear Complexity of Generalized Cyclotomic Quaternary Sequences with Length $2pq$

In this paper, the linear complexity over GF(r) of generalized cyclotomic quaternary sequences with period 2pq is determined, where r is an odd prime such that r ≥ 5 and r / ∈ {p, q}. The minimal value of the linear complexity is equal to 5pq+p+q+1 4 which is greater than the half of the period 2pq. According to the Berlekamp-Massey algorithm, these sequences are viewed as enough good for the use in cryptography. We show also that if the character of the extension field GF(r), r, is chosen so that ( r p )