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The estimate of the linear complexity of generalized cyclotomic binary and quaternary sequences with periods pn and 2pn

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Abstract

In this paper, first we consider the linear complexity of quaternary sequences over the finite ring of order four and the finite field of order four. These sequences are constructed from new generalized cyclotomic classes modulo pn. Second, we study the linear complexity of new generalized cyclotomic binary sequences of period 2pn recently proposed by Ouyang et al. (Des. Codes Cryptogr. 87(5), 1–12 2019). We generalized results presented in this work and discuss the author’s conjecture. In conclusion, we again derive the linear complexity of quaternary sequences with period 2pn over the finite ring of order four and the finite field of order four. We use generalized cyclotomic classes modulo 2pn to define these sequences.

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

    Vladimir Edemskiy & Nikita Sokolovskiy

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  1. Vladimir Edemskiy
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  2. Nikita Sokolovskiy
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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 and Nikita Sokolovskiy are supported by RFBR and NSFC according to the research project No. 19-51-53003.

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Edemskiy, V., Sokolovskiy, N. The estimate of the linear complexity of generalized cyclotomic binary and quaternary sequences with periods pn and 2pn. Cryptogr. Commun. 14, 395–414 (2022). https://doi.org/10.1007/s12095-021-00534-7

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  • DOI: https://doi.org/10.1007/s12095-021-00534-7

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