Optimal Frequency-Hopping Sequence Sets Based on Cyclotomy

被引：7
|
作者：
Xu, Shanding [1 ,2 ]
Cao, Xiwang [1 ,3 ]
Xu, Guangkui [1 ,4 ]
机构：
[1] Nanjing Univ Aeronaut & Astronaut, Sch Math Sci, Nanjing 210016, Jiangsu, Peoples R China
[2] Nanjing Inst Technol, Dept Math & Phys, Nanjing 211167, Jiangsu, Peoples R China
[3] Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China
[4] Huainan Normal Univ, Sch Math Sci, Huainan 232038, Peoples R China
来源：
INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE | 2016年 / 27卷 / 04期
基金：
美国国家科学基金会;
关键词：
Frequency-hopping sequence; maximal Hamming correlation; average Hamming correlation; generalized cyclotomy; OPTIMAL HAMMING CORRELATION; CONSTRUCTIONS; BOUNDS;
D O I：
10.1142/S012905411650009X
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this paper, a kind of generalized cyclotomy with respect to the square of a prime is presented and the properties of the corresponding generalized cyclotomic numbers are investigated. Based on the generalized cyclotomy, a class of frequency-hopping sequence (FHS) set is constructed. By means of some basic properties of the generalized cyclotomy, we derive the Hamming correlation distribution of the new set. The results show that the proposed FHS set is optimal with regard to the average Hamming correlation (AHC) bound. By choosing suitable parameters, the construction also leads to the optimal FHS set and the optimal FHSs with regard to the maximum Hamming correlation (VIIIC) bound and Lempel-Greenberger bound, respectively.
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页码：443 / 462
页数：20
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