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Expected values for the rational complexity of finite binary sequences

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Abstract

2-Adic complexity plays an important role in cryptology. It measures the difficulty of outputting a binary sequence using a feedback with carry shift register. This paper studies the 2-adic complexity of finite sequences by investigating the corresponding rational complexity whose logarithm to the base 2 is just equal to the 2-adic complexity. Experiments show that the logarithm to the base 2 of the expected values for rational complexity is a good approximation to the expected values for the 2-adic complexity. Both a nontrivial lower bound and a nontrivial upper bound on the expected values for the rational complexity of finite sequences are given in the paper. In particular, the lower bound is much better than the upper bound.

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Authors and Affiliations

  1. Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, People’s Republic of China

    Tian Tian & Wen-Feng Qi

  2. State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, People’s Republic of China

    Wen-Feng Qi

Authors
  1. Tian Tian
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  2. Wen-Feng Qi
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Correspondence to Wen-Feng Qi.

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Communicated by P. Wild.

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Tian, T., Qi, WF. Expected values for the rational complexity of finite binary sequences. Des. Codes Cryptogr. 55, 65–79 (2010). https://doi.org/10.1007/s10623-009-9331-x

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  • DOI: https://doi.org/10.1007/s10623-009-9331-x

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