On the Error Linear Complexity of Some Generalized Cyclotomic Sequences of Order Two of Period pq

Linear complexity is an important pseudo-random measure of the keystream sequence in a stream cipher system. The error linear complexity is employed to measure the stability of the linear complexity, which means the minimal linear complexity by changing few bit of the original keystream sequence. This paper contributes to calculating the linear complexity of a famous generalized cyclotomic sequences of period pq defined by Ding and Helleseth. We give the linear complexity of these sequences in a new way, and calculate further the 1-error linear complexity of them. The result shows that the sequences have good stability in terms of linear complexity.