Fast Multi-Sequence Shift-Register Synthesis with the Euclidean Algorithm

Abstract

International audienceFeng and Tzeng's generalization of the Extended Euclidean Algorithm synthesizes the shortest--length linear feedback shift--register for \$s \geq 1\$ sequences, where each sequence has the 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 \$\ONsn^2\$. An acceleration based on the Divide and Conquer strategy is proposed and it is proven that subquadratic time complexity is achieved