A Class of Frequency-Hopping Sequences Set with a Multiple of Prime Number Length

XU Shan-ding; CAO Xi-wang; XU Guang-kui

doi:10.3969/j.issn.0372-2112.2015.10.008

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A Class of Frequency-Hopping Sequences Set with a Multiple of Prime Number Length

更新时间：2025-07-16

- A Class of Frequency-Hopping Sequences Set with a Multiple of Prime Number Length
- Acta Electronica Sinica Vol. 43, Issue 10, Pages: 1930-1935(2015)
- 作者机构：
  
  1. 南京工程学院数理部,江苏,南京,211167
  2. 南京航空航天大学数学系,江苏,南京,211106
  3. 中国科学院信息工程研究所信息安全国家重点实验室,北京,100093
  4. 淮南师范学院数学与计算科学系,安徽,淮南,232038
  5. 南京工程学院数理部,江苏,南京,211167
  6. 南京航空航天大学数学系,江苏,南京,211106
  7. 中国科学院信息工程研究所信息安全国家重点实验室,北京,100093
  8. 淮南师范学院数学与计算科学系,安徽,淮南,232038
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.11371011);Natural Science Research Project of Colleges and Universities in Jiangsu Province (No.14KJB110008);Research Fund Project of Nanjing Institute of Technology (No.QKJA201307)
- DOI：10.3969/j.issn.0372-2112.2015.10.008
  CLC： TN914.43
- Published：2015
- 稿件说明：
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XU Shan-ding, CAO Xi-wang, XU Guang-kui. A Class of Frequency-Hopping Sequences Set with a Multiple of Prime Number Length[J]. Acta Electronica Sinica, 2015, 43(10): 1930-1935.
DOI：

XU Shan-ding, CAO Xi-wang, XU Guang-kui. A Class of Frequency-Hopping Sequences Set with a Multiple of Prime Number Length[J]. Acta Electronica Sinica, 2015, 43(10): 1930-1935. DOI： 10.3969/j.issn.0372-2112.2015.10.008.

摘要

跳频技术具有抗干扰、抗截获、码分多址和频带共享等优点

在军事无线电通信、民用移动通信、现代雷达和声纳等电子系统中具有重要的应用.其中跳频序列是跳频系统中不可或缺的一部分.本文基于有限域上的分圆法和中国剩余定理

首先构造了一类周期为素数倍数的跳频序列族

随后利用分圆数的性质导出了此序列族的汉明相关值.研究结果表明

该序列族不仅关于Peng-Fan界是最优的

而且每个序列关于Lempel-Greenberger界也是最优(或次最优)的.另外

已有的基于分圆法的最优跳频序列构造是本文的特例.

Abstract

Frequency-hopping spread spectrum (FHSS) systems

with properties of anti-jamming

anti-intercept

code division multiple access (CDMA)

channel sharing

etc

are usually applied in military radio communication

mobile communication

modern radar and sonar echolocation systems.Frequency-hopping sequences (FHS) is an integral part of FHSS systems.Based on the cyclotomy over the finite field and the Chinese remainder theorem

a class of FHSs set with a multiple of prime number length is constructed and the Hamming correlations of the new set are derived by some basic properties of the cyclotomic numbers.The results show that the proposed set is optimal with respect to the Peng-Fan bound and each FHS of the set is optimal or near optimal with respect to the Lempel-Greenberger bound.Furthermore

the previous constructions of optimal FHS sets based on cyclotomy are special cases of this paper.

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