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

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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) = 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 \((x^2+x+1)^{2^v}\).

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Acknowledgement

The author would like to thank the anonymous referee for suggestions that helped to improve the paper.

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  1. Sabancı University, MDBF, Orhanlı, Tuzla, 34956, İstanbul, Turkey

    Wilfried Meidl

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  1. Wilfried Meidl
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Correspondence to Wilfried Meidl.

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Meidl, W. How to determine linear complexity and k-error linear complexity in some classes of linear recurring sequences. Cryptogr. Commun. 1, 117–133 (2009). https://doi.org/10.1007/s12095-008-0007-6

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  • DOI: https://doi.org/10.1007/s12095-008-0007-6

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