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Generalized cyclotomic sequences of period pq have several desirable randomness properties if the two primes p and q are chosen properly. In particular, Ding deduced the exact formulas for the autocorrelation and the linear complexity of these sequences of order 2. In this paper, we consider the generalized sequences of order 4. Under certain conditions, the linear complexity of these sequences is developed over a finite field Fl. The results show that, in many cases, they have high linear complexity.

Linear Complexity of Generalized Cyclotomic Sequences of Order 4 over Fl