Linear complexity and k-error linear complexity are the important measures for sequences in stream ciphers. This paper discusses the asymptotic behavior of the normalized k-error linear complexity L n,k (s)/n of random binary sequences s, which is based on one of Niederreiter's open problems. For k = nθ , where 0 ≤ θ ≤ 1/2 is a fixed ratio, the lower and upper bounds on accumulation points of L n,k (s)/n are derived, which holds with probability 1. On the other hand, for any fixed k it is shown that lim n→∞ L n,k (s)/n = 1/2 holds with probability 1. The asymptotic bounds on the expected value of normalized k-error linear complexity of binary sequences are also presented.
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