How to determine linear complexity and k-error linear complexity in some classes of linear recurring sequences

Abstract

Several fast algorithms for the determination of the linear complexity of d-periodic sequences over a finite field \({\mathbb F}_q\), i.e. sequences with characteristic polynomial f(x) = xd − 1, have been proposed in the literature. In this contribution fast algorithms for determining the linear complexity of binary sequences with characteristic polynomial f(x) = (x − 1)d for an arbitrary positive integer d, and \(f(x) = (x^2+x+1)^{2^v}\) are presented. The result is then utilized to establish a fast algorithm for determining the k-error linear complexity of binary sequences with characteristic polynomial \((x^2+x+1)^{2^v}\).