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Distribution of one-error linear complexity of binary sequences for arbitrary prime period

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Abstract

Complexity measures for sequences, such as the linear complexity and the k-error linear complexity, play an important role in stream ciphers. This contribution studies the distribution of 1-error linear complexity of binary sequences with arbitrary prime period. For any odd prime N, the authors present all possible values of 1-error linear complexity of N-periodic binary sequences, and derive the exact formulas to count the number of N-periodic binary sequences with any given 1-error linear complexity.

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Authors and Affiliations

  1. Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, 450002, China

    Lin Tan, Wenfeng Qi & Hong Xu

Authors
  1. Lin Tan
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  2. Wenfeng Qi
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  3. Hong Xu
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Corresponding author

Correspondence to Lin Tan.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 61070178, 61100200, and 60833008.

This paper was recommended for publication by Editor Lei HU.

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Tan, L., Qi, W. & Xu, H. Distribution of one-error linear complexity of binary sequences for arbitrary prime period. J Syst Sci Complex 25, 1223–1233 (2012). https://doi.org/10.1007/s11424-012-1101-6

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  • DOI: https://doi.org/10.1007/s11424-012-1101-6

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