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The symmetric 2-adic complexity of sequences with optimal autocorrelation magnitude and length 8q

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This paper is devoted to studying the symmetric 2-adic complexity of sequences with optimal autocorrelation magnitude and period 8q, where q is a prime satisfying q ≡ 5 (mod 8). These sequences were constructed by interleaving technique from Ding-Helleseth-Martinsen sequences and almost perfect binary sequences. They were presented by Krengel and Ivanov in 2016 and have been proved to have high linear complexity. Our result shows that they also have high symmetric 2-adic complexity.

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References

  1. Ding, C., Helleseth, T., Lam, K.: Several classes of sequences with three-level autocorrelation. IEEE Trans. Inf. Theory 45(7), 2606–2612 (1999)

    Article  MathSciNet  Google Scholar 

  2. Ding, C., Helleseth, T., Martinsen, H.: New families of binary sequences with optimal three-valued autocorrelation. IEEE Trans. Inf. Theory 47 (1), 428–433 (2001)

    Article  Google Scholar 

  3. Edemskiy, V.A., Minin, A.B.: Linear complexity of binary sequences with optimal autocorrelation magnitude of length. MMPAM’2019. IOP Conf. Series J. Phys. Conf. Series. 1352, 012013 (2019)

    Article  Google Scholar 

  4. Fan, C.: The linear complexity of a class of binary sequences with optimal autocorrelation. Des. Codes Crypt. 86, 2441–2450 (2018)

    Article  MathSciNet  Google Scholar 

  5. Hu, H.: Comments on a new method to compute the 2-adic complexity of binary sequences. IEEE Trans. Inform. Theory 60, 5803–5804 (2014)

    Article  MathSciNet  Google Scholar 

  6. Gong, G.: Theory and applications of q-ary interleaved sequences. IEEE Trans. Inform. Theory 41(2), 400–411 (1995)

    Article  MathSciNet  Google Scholar 

  7. Hu, H., Feng, D.: On the 2-adic complexity and the k-error 2-adic complexity of periodic binary sequences. IEEE Trans. Inf. Theory 54(2), 874–883 (2008)

    Article  MathSciNet  Google Scholar 

  8. Jungnickel, D., Pott, A.: Perfect and almost perfect sequences. Discret. Appl. Math. 95, 331–359 (1999)

    Article  MathSciNet  Google Scholar 

  9. Klapper, A., Goresky, M.: Cryptanalysis Based on 2-Adic Rational Approxiamtion. In: CRYPTO 1995, LNCS, 963, pp 262–273 (1995)

  10. Klapper, A., Goresky, M.: Feedback shift registers, 2-adic span, and combiners with memory. J. Cryptol. 10, 111–147 (1997)

    Article  MathSciNet  Google Scholar 

  11. Krengel, E.I., Ivanov, P.V.: Two costructions of binary sequences with optimal autocorrelationmagnitude. Electron. Lett. 52, 1457–1459 (2016)

    Article  Google Scholar 

  12. Langevin, P.H.: Some sequences with good autocorrelation properties. Finite Fields 168, 175–185 (1994)

    MathSciNet  MATH  Google Scholar 

  13. Li, N., Tang, X.: On the linear complexity of binary sequences of period 4N with optimal autocorrelation/magnitude. IEEE Trans. Inform. Theory 57, 7597–7604 (2011)

    Article  MathSciNet  Google Scholar 

  14. Sun, Y., Shen, H.: New binary sequences of length 4p with optimal autocorrelation magnitude. Ars Combinatoria 89, 255–262 (2008)

    MathSciNet  MATH  Google Scholar 

  15. Sun, Y., Wang, Q., Yan, T.: The exact autocorrelation distribution and 2-adic complexity of a class of binary sequences with almost optimal autocorrelation. Cryptogr. Commun. 10(3), 467–477 (2018)

    Article  MathSciNet  Google Scholar 

  16. Sun, Y., Yan, T., Chen, Z., Wang, L.: The 2-adic complexity of a class of binary sequences with optimal autocorrelation magnitude. Cryptogr. Commun. 12, 675–683 (2020)

    Article  MathSciNet  Google Scholar 

  17. Su, W., Yang, Y., Fan, C.: New optimal binary sequences with period 4p via interleaving Ding-Helleseth-Lam sequences. Designs Codes Cryptograp. 86, 1329–1338 (2018)

    Article  MathSciNet  Google Scholar 

  18. Tang, X., Ding, C.: New classes of balanced quaternary and almost balanced binary sequences with optimal autocorrelation value. IEEE Trans. Inform. Theory 56(3), 6398–6405 (2010)

    Article  MathSciNet  Google Scholar 

  19. Tang, X., Gong, G.: New constructions of binary sequences with optimal autocorrelation value/magnitude. IEEE Trans. Inform. Theory 56(12), 1278–1286 (2010)

    Article  MathSciNet  Google Scholar 

  20. Wolfmann, J.: Almost perfect autocorrelation sequences. IEEE Trans. Inf. Theory 38(4), 1412–1418 (1992)

    Article  MathSciNet  Google Scholar 

  21. Xiao, Z., Zeng, X., Sun, Z.: 2-Adic complexity of two classes of generalized cyclotomic binary sequences. Internationl. J. Foundat. Comput. Sci. 27 (7), 879–893 (2016)

    Article  MathSciNet  Google Scholar 

  22. Xiong, H., Qu, L., Li, C.: A new method to compute the 2-adic complexity of binary sequences. IEEE Trans. Inform. Theory 60, 2399–2406 (2014)

    Article  MathSciNet  Google Scholar 

  23. Xiong, H., Qu, L., Li, C.: 2-Adic complexity of binary sequences with interleaved structure. Finite Fields Their Appl. 33, 14–28 (2015)

    Article  MathSciNet  Google Scholar 

  24. Yang, M., Zhang, L., Feng, K.: On the 2-adic complexity of a class of binary sequences of period 4p with optimal autocorrelation magnitude. arXiv:1904.13012 (2019)

  25. Zhang, S., Yan, T.: Linear Complexity and Autocorrelation of two Classes of New Interleaved Sequences of Period 2N. arXiv:1801.08664 (2018)

  26. Zhang, L., Zhang, J., Yang, M., Feng, K.: On the 2-Adic Complexity of the Ding-Helleseth-Martinsen Binary Sequences. In: IEEE Trans. Inform. Theory. https://doi.org/10.1109/TIT.2020.2964171 (2020)

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Acknowledgements

The authors would like to thank the reviewers and editors for their detailed and constructive comments, which substantially improved the presentation of the paper.

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Authors and Affiliations

  1. Yaroslav-the-Wise Novgorod State University, Veliky Novgorod, Russia

    Vladimir Edemskiy

  2. College of Science, China University of Petroleum, Qingdao, Shandong, China

    Yuhua Sun

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  1. Vladimir Edemskiy
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  2. Yuhua Sun
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Correspondence to Vladimir Edemskiy.

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This article belongs to the Topical Collection: Sequences and Their Applications III Guest Editors: Chunlei Li, Tor Helleseth and Zhengchun Zhou

Vladimir Edemskiy is supported by RFBR and NSFC according to the research project No. 19-51-53003. Yuhua Sun is financially supported by the National Natural Science Foundation of China (No. 61902429), the Fundamental Research Funds for the Central Universities (No. 19CX02058A).

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Edemskiy, V., Sun, Y. The symmetric 2-adic complexity of sequences with optimal autocorrelation magnitude and length 8q. Cryptogr. Commun. 14, 183–199 (2022). https://doi.org/10.1007/s12095-021-00503-0

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  • DOI: https://doi.org/10.1007/s12095-021-00503-0

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