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2-Adic complexity of two constructions of binary sequences with period 4N and optimal autocorrelation magnitude

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Abstract

Three constructions of binary sequences with period 4N and optimal autocorrelation value or optimal autocorrelation magnitude have been presented by Tang and Gong based on interleaving technique. In this paper, the 2-adic complexity of the sequences with optimal autocorrelation magnitude constructed from the Legendre sequence pair or the twin-prime sequence pair is investigated. With the method proposed by Hu, we completely determine the 2-adic complexity of the sequences by calculating the exact autocorrelation distribution of the sequences and discussing the greatest common divisors. Results show that the 2-adic complexity of these sequences is either maximum or very close to maximum.

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Acknowledgements

The authors would like to thank the Editors and the anonymous referees for their valuable comments and helpful suggestions. This work was supported by the National Natural Science Foundation of China (Nos. 62072161, 12061027) and the Application Foundation Frontier Project of Wuhan Science and Technology Bureau (No. 2020010601012189)

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Authors and Affiliations

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

    Zibi Xiao

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

    Xiangyong Zeng

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  1. Zibi Xiao
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  2. Xiangyong Zeng
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Correspondence to Xiangyong Zeng.

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Xiao, Z., Zeng, X. 2-Adic complexity of two constructions of binary sequences with period 4N and optimal autocorrelation magnitude. Cryptogr. Commun. 13, 865–885 (2021). https://doi.org/10.1007/s12095-021-00498-8

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  • DOI: https://doi.org/10.1007/s12095-021-00498-8

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