On the k-Error Linear Complexity of Binary Sequences Derived from the Discrete Logarithm in Finite Fields

Abstract

Let Fq be the finite field with q=pr elements, where p is an odd prime. For the ordered elements ξ0,ξ1,…,ξq-1∈Fq, the binary sequence σ=(σ0,σ1,…,σq-1) with period q is defined over the finite field F2={0,1} as follows: σn=0, if n=0, (1-χ(ξn))/2, if 1≤n2 and we leave it open.