Design sequences with high linear complexity over finite fields using generalized cyclotomy (original) (raw)

Abstract

Based on the generalized cyclotomy theory, we design some classes of sequences with high linear complexity over the finite fields. First, we construct a new class of sequence from some generalized cyclotomic sequences of different orders with different prime powers period. Then we obtain the discrete Fourier transform, defining pairs and the linear complexity of the new sequences. Finally, we study the linear complexity of a special class of _q_−ary (q prime) sequences.

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Acknowledgments

The authors acknowledge the patient referees for their valuable and constructive comments which helped to improve this work.

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Authors and Affiliations

  1. Novgorod State University, Str. B. St. Petersburgskaya, 41, 173003, Veliky Novgorod, Russia
    Vladimir Edemskiy
  2. College of Mathematics and Information Science, Northwest Normal University, Lanzhou, Gansu, 730070, People’s Republic of China
    Xiaoni Du

Authors

  1. Vladimir Edemskiy
  2. Xiaoni Du

Corresponding author

Correspondence toVladimir Edemskiy.

Additional information

V. Edemskiy was supported by the Ministry of Education and Science of Russia as a part of state-sponsored project No. 1.949.2014/K. X. Du was partially supported by the National Natural Science Foundation of China (grant No. 61462077) and the Program for New Century Excellent Talents in University (NCET-12-0620).

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Edemskiy, V., Du, X. Design sequences with high linear complexity over finite fields using generalized cyclotomy.Cryptogr. Commun. 9, 683–691 (2017). https://doi.org/10.1007/s12095-016-0209-2

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Mathematics Subject Classification (2010)