On the k-error linear complexity of l-sequences

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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.




Tan, L., & Qi, W. F. (2010). On the k-error linear complexity of l-sequences. Finite Fields and Their Applications, 16(6), 420–435. https://doi.org/10.1016/j.ffa.2010.07.002

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