Fast multi-sequence shift-register synthesis with the Euclidean algorithm

Feng and Tzeng’s generalization of the Extended Euclidean Algorithm synthesizes the shortest–length linear feedback shift–register for s ≥ 1 sequences, where each sequence has the same length n. In this contribution, it is shown that Feng and Tzeng’s algorithm which solves this multi–sequence shift–register problem has time complexity O(sn2). An acceleration based on the Divide and Conquer strategy is proposed and it is proven that subquadratic time complexity is achieved.