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A new family of polyphase sequences with low correlation

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Abstract

Sequences with low correlation have important applications in communications, radar, cryptography, and also in compressed sensing. The ultimate objective of this paper is to design a new family of polyphase sequences with low correlation. Our main contribution is the construction of such a family using additive and multiplicative characters over Galois rings. The proposed sequences have lengths N = pm − 1, family size M = pkm − 1, and a maximum magnitude \(\theta _{\max \limits }=p^{k-1}\sqrt {p^{m}}\), where k is an integer with 1 ≤ k < m.

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Acknowledgements

The authors deeply thank the Associate Editor and the anonymous reviewers for their valuable comments which have improved the quality and the presentation of the paper. The work of Z. Gu and Z. Zhou was supported by the National Natural Science Foundation of China (NSFC) project under Grant 62071397.

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Authors and Affiliations

  1. School of Information Science and Technology, Southwest Jiaotong University, Chengdu, 611756, China

    Zhi Gu & Zhengchun Zhou

  2. State Key Laboratory of Cryptology, Beijing, 100878, China

    Zhi Gu & Zhengchun Zhou

  3. Department of Mathematics, University of Paris VIII, F-93526, Saint-Denis, France

    Sihem Mesnager

  4. University Sorbonne Paris Cité, LAGA, UMR 7539, CNRS, 93430, Villetaneuse, France

    Sihem Mesnager

  5. Télécom Paris, 91120, Palaiseau, France

    Sihem Mesnager

  6. Department of Computing and Information Systems, University of Melbourne, Melbourne, VIC, 3010, Australia

    Udaya Parampalli

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  1. Zhi Gu
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  2. Zhengchun Zhou
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  3. Sihem Mesnager
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  4. Udaya Parampalli
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Correspondence to Sihem Mesnager.

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Gu, Z., Zhou, Z., Mesnager, S. et al. A new family of polyphase sequences with low correlation. Cryptogr. Commun. 14, 135–144 (2022). https://doi.org/10.1007/s12095-021-00522-x

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