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 $\F_q$, 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 $(x^2+x+1)^{2^v}$.

Available Versions of this Item

• How to determine linear complexity and $k$-error linear complexity in some classes of linear recurring sequences. (deposited 07 Nov 2008 17:10) [Currently Displayed]
  • How to determine linear complexity and k-error linear complexity in some classes of linear recurring sequences. (deposited 29 Apr 2009 10:35)