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Linear complexity of generalized cyclotomic sequences of period \(2p^{m}\)

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Abstract

In this paper, we construct two generalized cyclotomic binary sequences of period \(2p^{m}\) based on the generalized cyclotomy and compute their linear complexity, showing that they are of high linear complexity when \(m\ge 2\).

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Acknowledgements

Y. O. would like to thank the Morningside Center of Mathematics for hospitality where part of this paper was written. We thank the referees for many helpful comments, especially for providing a counterexample for a previous conjecture about the linear complexity of sequences in the second class.

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Authors and Affiliations

  1. Wu Wen-Tsun Key Laboratory of Mathematics, School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, Anhui, China

    Yi Ouyang

  2. Key Laboratory of Electromagnetic Space Information, CAS, University of Science and Technology of China, Hefei, 230027, Anhui, China

    Xianhong Xie

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  1. Yi Ouyang
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  2. Xianhong Xie
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Correspondence to Xianhong Xie.

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Communicated by T. Helleseth.

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Partially supported by Anhui Initiative in Quantum Information Technologies (Grant No. AHY150200) and NSFC (Grant No. 11571328).

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Ouyang, Y., Xie, X. Linear complexity of generalized cyclotomic sequences of period \(2p^{m}\). Des. Codes Cryptogr. 87, 2585–2596 (2019). https://doi.org/10.1007/s10623-019-00638-5

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