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Symmetric 2-adic complexity of Tang–Gong interleaved sequences from generalized GMW sequence pair

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Abstract

Tang–Gong interleaved sequences constructed from the generalized GMW sequence pair are a class of binary sequences with optimal autocorrelation magnitude. In this paper, the symmetric 2-adic complexity of these sequences is investigated. We first derive a lower bound on their 2-adic complexity by extending the method proposed by Hu. Then, by analysing the algebraic structure of these sequences, a lower bound on their symmetric 2-adic complexity is obtained. Our result shows that the symmetric 2-adic complexity of these sequences is large enough to resist attacks with the rational approximation algorithm.

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Acknowledgements

The authors would like to thank the anonymous referees for their helpful comments and suggestions. The work of X. Zeng was supported by the National Natural Science Foundation of China under Grant 62072161, and by the Innovation Group Project of the Natural Science Foundation of Hubei Province of China under Grant 2023AFA021. The work of B. Yang, K. He and Z. Xiao was supported by the National Natural Science Foundation of China under Grant 12061027.

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Authors and Affiliations

  1. College of Science, Wuhan University of Science and Technology, Wuhan, 430081, Hubei, China

    Bo Yang, Kangkang He & Zibi Xiao

  2. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan, 430062, Hubei, China

    Xiangyong Zeng

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  1. Bo Yang
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  2. Kangkang He
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  3. Xiangyong Zeng
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  4. Zibi Xiao
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Contributions

B. Yang and Z. Xiao discussed and developed the basic idea. K. He performed calculations and drafted the manuscript. B. Yang verified the computation and revised the manuscript. X. Zeng and Z. Xiao supplemented the details of the article and polished it. All authors reviewed the manuscript.

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Correspondence to Zibi Xiao.

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The authors declare no competing interests.

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Communicated by J. Jedwab.

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Yang, B., He, K., Zeng, X. et al. Symmetric 2-adic complexity of Tang–Gong interleaved sequences from generalized GMW sequence pair. Des. Codes Cryptogr. (2024). https://doi.org/10.1007/s10623-024-01399-6

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  • DOI: https://doi.org/10.1007/s10623-024-01399-6

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