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Linear complexity of two classes of quaternary sequences based on sign alternation transformation

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Two classes of optimal quaternary sequences have been constructed by applying the sign alternation transform and Gray mapping to Legendre sequence pair, twin-prime sequence pair and GMW sequence pair. In this paper, a new method for investigating the linear complexity over finite field is proposed, and the exact values of the linear complexity over finite field \({\mathbb {F}}_4\) and Galois ring \({\mathbb {Z}}_4\) of the quaternary sequences are determined. The results show that their linear complexity are quite good.

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Acknowledgements

The authors wish to thank the referees for their detailed and very helpful comments and suggestions that much improved this paper. The works was supported by National Natural Science Foundation of China (Grant Nos. 61701343, U1404601, 11571094, 11971004), Humanity and Social Science Youth foundation of Ministry of Education of China (Grant Nos. 20YJC910009).

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Authors and Affiliations

  1. School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China

    Lu Zhao, Yongzhen Pei & Tianqing Cao

  2. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

    Jiao Du

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  1. Lu Zhao
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  2. Yongzhen Pei
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  3. Tianqing Cao
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  4. Jiao Du
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Correspondence to Lu Zhao.

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Zhao, L., Pei, Y., Cao, T. et al. Linear complexity of two classes of quaternary sequences based on sign alternation transformation. AAECC (2022). https://doi.org/10.1007/s00200-022-00559-2

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  • DOI: https://doi.org/10.1007/s00200-022-00559-2

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