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NHZ frequency hopping sequence sets under aperiodic Hamming correlation: Tighter bound and optimal constructions

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Abstract

In this paper, we first establish a new bound on no-hit-zone (NHZ) frequency hopping (FH) sequence sets under aperiodic Hamming correlation. The new bound is tighter than the bound on NHZ FH sequence sets under aperiodic Hamming correlation which was derived by Liu et al. (Electron. Lett. 54, 212–213, 2018). Then we construct a class of NHZ FH sequence sets under aperiodic Hamming correlation. They are optimal with respect to the new bound and have more flexible parameters than those in Liu et al. (Electron. Lett. 54, 212–213, 2018). Further, we give a construction of NHZ FH sequence sets with low aperiodic Hamming correlation value outside of NHZ which are also optimal with respect to the new bound.

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Acknowledgements

The authors are very grateful to the anonymous reviewers and the Associate Editor for their valuable suggestions and comments that help to improve the paper. X. Liu was supported in part by the National Natural Science Foundation of China (Grant No. 61901288) and in part by the Fundamental Research Funds for the Central Universities (Grant No. 2019SCU12004). S. Hong was supported in part by the National Natural Science Foundation of China (Grant No. 11771304). Q. Zeng was supported in part by the National Natural Science Foundation of China (Grant No. 61701328). L. Zhou was supported in part by the National Natural Science Foundation of China (Grant No. 61901096).

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Authors and Affiliations

  1. College of Electrical Engineering, Sichuan University, 610065, Chengdu, China

    Xing Liu & Qi Zeng

  2. College of Mathematics, Sichuan University, 610064, Chengdu, China

    Xing Liu & Shaofang Hong

  3. School of Electronic and Information Engineering, University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan, China

    Limengnan Zhou

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  1. Xing Liu
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  2. Shaofang Hong
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  3. Qi Zeng
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  4. Limengnan Zhou
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Correspondence to Xing Liu.

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This article belongs to the Topical Collection: Sequences and Their Applications III

Guest Editors: Chunlei Li, Tor Helleseth and Zhengchun Zhou

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Liu, X., Hong, S., Zeng, Q. et al. NHZ frequency hopping sequence sets under aperiodic Hamming correlation: Tighter bound and optimal constructions. Cryptogr. Commun. 14, 347–356 (2022). https://doi.org/10.1007/s12095-021-00527-6

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  • DOI: https://doi.org/10.1007/s12095-021-00527-6

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