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Generalized methods to construct low-hit-zone frequency-hopping sequence sets and optimal constructions

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Abstract

In a quasi-synchronous frequency-hopping multiple-access system, relative time delay between different users within a zone around the origin can be allowed. Therefore, frequency-hopping sequence (FHS) sets with low-hit-zone (LHZ) have attracted great interest of many related scholars. Moreover, on account of the limited synchronous time or hardware complexity, the periodic partial Hamming correlation (PPHC) plays a major role in determining the synchronization performance. In this paper, we first present three new generalized methods to construct LHZ-FHS sets via Cartesian product. Meanwhile, we pay our attention to the maximum periodic Hamming correlation (PHC) of the constructed LHZ-FHS sets in the first generalized method, and to the maximum PPHC of the constructed LHZ-FHS sets in the rest generalized methods. In addition, we also introduce five new classes of optimal LHZ-FHS sets based on these three generalized methods.

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Acknowledgments

This work was supported by National Science Foundation of China (Grant No. 61271244), National High Technology Research and Development Program of China (863 Program) (Grant No. 2015AA01A705), and National Science Foundation of China (Grant No. 61571373). Limengnan Zhou and Hongbin Liang are corresponding authors.

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Authors and Affiliations

  1. Provincial Key Lab of Information Coding and Transmission, Institute of Mobile Communications, Southwest Jiaotong University, Chengdu, China

    Limengnan Zhou, Daiyuan Peng, Changyuan Wang & Hongyu Han

  2. School of Transportation and Logistics, Provincial Key Lab of Information Coding and Transmission, Institute of Mobile Communications, Southwest Jiaotong University, Chengdu, China

    Hongbin Liang

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  1. Limengnan Zhou
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  2. Daiyuan Peng
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  3. Hongbin Liang
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  4. Changyuan Wang
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  5. Hongyu Han
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Correspondence to Limengnan Zhou.

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Zhou, L., Peng, D., Liang, H. et al. Generalized methods to construct low-hit-zone frequency-hopping sequence sets and optimal constructions. Cryptogr. Commun. 9, 707–728 (2017). https://doi.org/10.1007/s12095-017-0211-3

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  • DOI: https://doi.org/10.1007/s12095-017-0211-3

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Mathematics Subject Classification (2010)