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AIMS Mathematics

2023, Volume 8, Issue 12: 29158-29170. doi: 10.3934/math.20231493
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Optimal and near-optimal frequency-hopping sequences based on Gaussian period

  • 1.
    School of Science, Xi'an University of Architecture and Technology, Caosi East Road, Xi'an, Shaanxi, 710311, China
  • 2.
    Hubei Key Laboratory of Applied Mathematics, School of Cyber Science and Technology, Hubei University, Wuhan, Hubei, 430062, China
  • Received: 13 August 2023 Revised: 09 October 2023 Accepted: 20 October 2023 Published: 26 October 2023

  • MSC : 11T22, 94A60

  • Frequency-hopping sequences (FHSs) have a decisive influence on the whole frequency-hopping communication system. The Hamming correlation function plays an important role in evaluating the performance of FHSs. Constructing FHS sets that meet the theoretical bounds is crucial for the research and development of frequency-hopping communication systems. In this paper, three new classes of optimal FHSs based on trace functions are constructed. Two of them are optimal FHSs and the corresponding periodic Hamming autocorrelation value is calculated by using the known Gaussian period. It is shown that the new FHSs are optimal according to the Lempel-Greenberger bound. The third class of FHSs is the near-optimal FHSs.

    Citation: Yan Wang, Yanxi Fu, Nian Li, Huanyu Wang. Optimal and near-optimal frequency-hopping sequences based on Gaussian period[J]. AIMS Mathematics, 2023, 8(12): 29158-29170. doi: 10.3934/math.20231493

    Related Papers:

  • Frequency-hopping sequences (FHSs) have a decisive influence on the whole frequency-hopping communication system. The Hamming correlation function plays an important role in evaluating the performance of FHSs. Constructing FHS sets that meet the theoretical bounds is crucial for the research and development of frequency-hopping communication systems. In this paper, three new classes of optimal FHSs based on trace functions are constructed. Two of them are optimal FHSs and the corresponding periodic Hamming autocorrelation value is calculated by using the known Gaussian period. It is shown that the new FHSs are optimal according to the Lempel-Greenberger bound. The third class of FHSs is the near-optimal FHSs.


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