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

Alexander Zeh, Antonia Wachter

Abstract: Feng and Tzeng's generalization of the Extended Euclidean Algorithmsynthesizes the shortest-length linear feedback shift-register for $s \geq 1$ 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 $\mathcal{O}(sn^2)$. An acceleration based on the Divide and Conquer strategy is proposed and it is proven that subquadratic time complexity is achieved.