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Volume 26
Issue 11
10.3390/e26110935
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Article

A Construction of Optimal One-Coincidence Frequency-Hopping Sequences via Generalized Cyclotomy

by
Minfeng Shao
1,* and
Ying Miao
2
1
School of Computer and Software Engineering, Xihua University, Chengdu 610039, China
2
Graduate School of Systems and Information Engineering, University of Tsukuba, Tennodai 1-1-1, Tsukuba 305-8573, Japan
*
Author to whom correspondence should be addressed.
Entropy 2024, 26(11), 935; https://doi.org/10.3390/e26110935
Submission received: 10 October 2024 / Revised: 29 October 2024 / Accepted: 30 October 2024 / Published: 31 October 2024
(This article belongs to the Special Issue Advances in Information and Coding Theory, the Third Edition)
Versions Notes

Abstract

Frequency-hopping sequences (FHSs) with low Hamming correlation are essential for synchronization and multiple-access communication systems. In this paper, we propose a novel construction of FHSs using generalized cyclotomy. Our results reveal that the constructed FHSs exhibit a one-coincidence property, meaning that the smallest correlation between different FHSs, aside from the trivial case, is minimized. Additionally, the new sets of FHSs achieve an optimal size in relation to a known theoretical bound.
Keywords: frequency-hopping sequence; Hamming correlation; Peng–Fan bound; generalized cyclotomy frequency-hopping sequence; Hamming correlation; Peng–Fan bound; generalized cyclotomy

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MDPI and ACS Style

Shao, M.; Miao, Y. A Construction of Optimal One-Coincidence Frequency-Hopping Sequences via Generalized Cyclotomy. Entropy 2024, 26, 935. https://doi.org/10.3390/e26110935

AMA Style

Shao M, Miao Y. A Construction of Optimal One-Coincidence Frequency-Hopping Sequences via Generalized Cyclotomy. Entropy. 2024; 26(11):935. https://doi.org/10.3390/e26110935

Chicago/Turabian Style

Shao, Minfeng, and Ying Miao. 2024. "A Construction of Optimal One-Coincidence Frequency-Hopping Sequences via Generalized Cyclotomy" Entropy 26, no. 11: 935. https://doi.org/10.3390/e26110935

APA Style

Shao, M., & Miao, Y. (2024). A Construction of Optimal One-Coincidence Frequency-Hopping Sequences via Generalized Cyclotomy. Entropy, 26(11), 935. https://doi.org/10.3390/e26110935

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