Linear Complexity of Generalized Cyclotomic Sequences of Order 4 over Fl

Abstract

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 of order 4 is developed over a finite field F l . Results show that in many cases they have high linear complexity.