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The 2-adic complexity of Yu-Gong sequences with interleaved structure and optimal autocorrelation magnitude

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Abstract

In 2008, a class of binary sequences of period \(N=4(2^k-1)(2^k+1)\) with optimal autocorrelation magnitude has been presented by Yu and Gong based on an m-sequence, the perfect sequence (0, 1, 1, 1) of period 4 and interleaving technique. In this paper, we study the 2-adic complexity of these sequences. Our result shows that it is larger than \(N-2\lceil \mathrm {log}_2N\rceil +4\) (which is far larger than N/2) and could attain the maximum value N if suitable parameters are chosen, i.e., the 2-adic complexity of this class of interleaved sequences is large enough to resist the Rational Approximation Algorithm.

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Authors and Affiliations

  1. College of Sciences, China University of Petroleum, Qingdao, 266555, Shandong, China

    Yuhua Sun & Tongjiang Yan

  2. School of Computer Science and Technology, Tiangong University, Tianjin, 300387, China

    Qiuyan Wang

Authors
  1. Yuhua Sun
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  2. Tongjiang Yan
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  3. Qiuyan Wang
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Correspondence to Yuhua Sun.

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Communicated by T. Helleseth.

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This work is financially supported by the National Natural Science Foundation of China (Nos. 61902429, 11775306), the Fundamental Research Funds for the Central Universities (No. 19CX02058A), Shandong Provincial Natural Science Foundation of China (No. ZR2019MF070).

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Sun, Y., Yan, T. & Wang, Q. The 2-adic complexity of Yu-Gong sequences with interleaved structure and optimal autocorrelation magnitude . Des. Codes Cryptogr. 89, 695–707 (2021). https://doi.org/10.1007/s10623-020-00841-9

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  • DOI: https://doi.org/10.1007/s10623-020-00841-9

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