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New frequency-hopping sequence sets with good parameters under aperiodic hamming correlation

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Abstract

In this paper, two constructions of frequency-hopping sequence (FHS for short) sets with respect to aperiodic Hamming correlation (AHC for short) are presented. Based on the presented constructions, we obtain several classes of optimal or near optimal FHS sets from cyclic codes and some known FHS sets with periodic partial Hamming correlation (PPHC for short), and explicitly determine their parameters. Moreover, the parameters of the obtained FHS sets are new and have large family size.

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Acknowledgments

The authors are very grateful to the reviewers and the Editor, for their comments and suggestions that improved the presentation and quality of this paper. This research was supported by the Basic Research Project of Science and Technology Plan of Guangzhou city of China under grant number 202102020888, the National Natural Science Foundation of China under grant numbers 12171162, 11971175, 12141108 and 61971243, the National Key Research and Development Program of China under grant number 2018YFA0704703, and the Natural Science Foundation of Tianjin under grant number 20JCZDJC00610.

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Authors and Affiliations

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

    Wenjuan Yin

  2. College of Mathematics and Informatics, South China Agricultural University, Guangzhou, 510642, China

    Can Xiang

  3. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, China

    Fang-Wei Fu

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  1. Wenjuan Yin
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  2. Can Xiang
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  3. Fang-Wei Fu
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Correspondence to Can Xiang.

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Yin, W., Xiang, C. & Fu, FW. New frequency-hopping sequence sets with good parameters under aperiodic hamming correlation. Cryptogr. Commun. 15, 159–169 (2023). https://doi.org/10.1007/s12095-022-00596-1

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