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Linear Complexity of Generalized Cyclotomic Sequences with Period \(p^{n}q^{m}\)

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Arithmetic of Finite Fields (WAIFI 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13638))

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Abstract

Linear complexity is a very important merit factor for measuring the unpredictability of pseudo-random sequences for applications. The higher the linear complexity, the better the unpredictability of a sequence. In this paper, we continue the investigation of generalized cyclotomic sequences constructed by new generalized cyclotomy presented by Zeng et al. In detail, we consider the new generalized cyclotomic sequence with period \(p^nq^m\) where p, q are odd distinct primes and n, m are natural numbers. It is shown that these sequences have high linear complexity. Finally, we also give some examples to illustrate the correctness of our results.

V. Edemskiy was supported by Russian Science Foundation according to the research project No. 22-21-00516, https://rscf.ru/en/project/22-21-00516/. C. Wu was partially supported by the Projects of International Cooperation and Exchange NSFC-RFBR No. 61911530130, by the Natural Science Foundation of Fujian Province No. 2020J01905.

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Notes

  1. 1.

    The order of 2 modulo p is the least positive integer T such that \(2^T\equiv 1\pmod {p}\).

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Authors and Affiliations

  1. Department of Applied Mathematics and Informatics, Yaroslav-the-Wise Novgorod State University, Veliky Novgorod, 173003, Russia

    Vladimir Edemskiy

  2. Fujian Key Laboratory of Financial Information Processing, Putian University, Putian, Fujian, 351100, China

    Chenhuang Wu

Authors
  1. Vladimir Edemskiy
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  2. Chenhuang Wu
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Corresponding author

Correspondence to Chenhuang Wu .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Paris VIII, Paris, France

    Sihem Mesnager

  2. School of Mathematics, Southwest Jiaotong University, Chengdu, China

    Zhengchun Zhou

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Edemskiy, V., Wu, C. (2023). Linear Complexity of Generalized Cyclotomic Sequences with Period \(p^{n}q^{m}\). In: Mesnager, S., Zhou, Z. (eds) Arithmetic of Finite Fields. WAIFI 2022. Lecture Notes in Computer Science, vol 13638. Springer, Cham. https://doi.org/10.1007/978-3-031-22944-2_21

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  • DOI: https://doi.org/10.1007/978-3-031-22944-2_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22943-5

  • Online ISBN: 978-3-031-22944-2

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