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

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Official URL: http://dx.doi.org/10.1007/s12095-008-0007-6

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) = x d  − 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 $(x^2+x+1)^{2^v}$.