On the k-error linear complexity of l-sequences

Abstract

This paper studies the stability of the linear complexity of l-sequences. Let s- be an l-sequence with linear complexity attaining the maximum per(s-)/2+1. A tight lower bound and an upper bound on minerror(s-), i.e., the minimal value k for which the k-error linear complexity of s- is strictly less than its linear complexity, are given. In particular, for an l-sequence s- based on a prime number of the form 2r+1, where r is an odd prime number with primitive root 2, it is shown that minerror(s-) is very close to r, which implies that this kind of l-sequences have very stable linear complexity. © 2010 Elsevier Inc.