Abstract
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 \({L_{n,k}(\underline{s})/n}\) of random binary sequences \({\underline{s}}\) , which is based on one of Niederreiter’s open problems. For k = n θ, where 0 ≤ θ ≤ 1/2 is a fixed ratio, the lower and upper bounds on accumulation points of \({L_{n,k}(\underline{s})/n}\) are derived, which holds with probability 1. On the other hand, for any fixed k it is shown that \({\lim_{n\rightarrow\infty} L_{n,k}(\underline{s})/n = 1/2}\) 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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Communicated by T. Helleseth.
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Tan, L., Qi, WF. & Xu, H. Asymptotic analysis on the normalized k-error linear complexity of binary sequences. Des. Codes Cryptogr. 62, 313–321 (2012). https://doi.org/10.1007/s10623-011-9519-8
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DOI: https://doi.org/10.1007/s10623-011-9519-8