On the k-error linear complexity of cyclotomic sequences

Exact values and bounds on the k-error linear complexity of p-periodic sequences which are constant on the cyclotomic classes are determined. This family of sequences includes sequences of discrete logarithms, Legendre sequences and Hall's sextic residue sequence

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

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 $(x^2+x+1)^{2^v}$