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Linear Complexity and Trace Representation of New Ding Generalized Cyclotomic Sequences with Period pq and Order Two

Author

Listed:
  • Jiang Ma

    (School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China)

  • Wei Zhao

    (School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China)

  • Yanguo Jia

    (School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China)

  • Xiumin Shen

    (School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China)

  • Haiyang Jiang

    (School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China)

Abstract

Linear complexity is an important property to measure the unpredictability of pseudo-random sequences. Trace representation is helpful for analyzing cryptography properties of pseudo-random sequences. In this paper, a class of new Ding generalized cyclotomic binary sequences of order two with period pq is constructed based on the new segmentation of Ding Helleseth generalized cyclotomy. Firstly, the linear complexity and minimal polynomial of the sequences are investigated. Then, their trace representation is given. It is proved that the sequences have larger linear complexity and can resist the attack of the Berlekamp–Massey algorithm. This paper also confirms that generalized cyclotomic sequences with good randomness may be obtained by modifying the characteristic set of generalized cyclotomy.

Suggested Citation

  • Jiang Ma & Wei Zhao & Yanguo Jia & Xiumin Shen & Haiyang Jiang, 2021. "Linear Complexity and Trace Representation of New Ding Generalized Cyclotomic Sequences with Period pq and Order Two," Mathematics, MDPI, vol. 9(18), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2285-:d:637194
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