Cryptography and Communications

, Volume 1, Issue 1, pp 117–133

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


DOI: 10.1007/s12095-008-0007-6

Cite this article as:
Meidl, W. Cryptogr. Commun. (2009) 1: 117. doi: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) = 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 \((x^2+x+1)^{2^v}\).


Linear complexityk-error linear complexityAlgorithmLinear recurring sequencesStream cipher

Mathematics Subject Classifications (2000)


Copyright information

© Springer Science + Business Media, LLC 2008

Authors and Affiliations

  1. 1.Sabancı University, MDBFİstanbulTurkey