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Constructions of low-hit-zone frequency hopping sequence sets from cyclic codes

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Low-hit-zone frequency hopping sequence (LHZ-FHS) sets having optimal Hamming correlation are desirable in quasi-synchronous communication systems. In this paper, we first derive a new bound on maximum nontrivial Hamming correlation of LHZ-FHS sets from the famous Singleton bound in error correcting code literature, then obtain a general construction of LHZ-FHS sets from cyclic codes. Especially, two classes of LHZ-FHS sets meeting the new bound are constructed from punctured Reed-Solomon codes.

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Acknowledgements

The authors are very grateful to the Editor and the anonymous reviewer for careful reading and invaluable suggestions that improved the quality of this paper. This work was supported by the Natural Science Foundation of China under Grant 11971395, and was supported by the Projects of Central Government to Guide Local Scientific and Technological Development under Grant 2021ZYD0001.

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Authors and Affiliations

  1. School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, China

    Cuiling Fan & Xiaoxiao Cui

  2. School of Economics and Information Engineering, Southwestern University of Finance and Economics, Chengdu, 610074, China

    Wei Su

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  1. Cuiling Fan
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  2. Xiaoxiao Cui
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Correspondence to Wei Su.

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Fan, C., Cui, X. & Su, W. Constructions of low-hit-zone frequency hopping sequence sets from cyclic codes. AAECC 35, 691–701 (2024). https://doi.org/10.1007/s00200-022-00581-4

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  • DOI: https://doi.org/10.1007/s00200-022-00581-4

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