电子学报 ›› 2015, Vol. 43 ›› Issue (10): 1930-1935.DOI: 10.3969/j.issn.0372-2112.2015.10.008

• 学术论文 • 上一篇    下一篇

一类周期为素数倍数的跳频序列族

徐善顶1,2, 曹喜望2,3, 许广魁2,4   

  1. 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
  • 收稿日期:2014-10-10 修回日期:2015-02-04 出版日期:2015-10-25
    • 作者简介:
    • 徐善顶 男,1979年11月出生于山东省兖州市.现为南京航空航天大学数学系博士研究生.主要研究方向为代数编码及信息安全.E-mail:sdxzx11@163.com;曹喜望 男,1965年06月出生于湖北省麻城市.现为南京航空航天大学教授、博士生导师.主要研究方向为代数组合论,代数密码学.E-mail:xwcao@nuaa.edu.cn
    • 基金资助:
    • 国家自然科学基金项目 (No.11371011); 江苏省高校自然科学研究面上项目 (No.14KJB110008); 南京工程学院校级科研基金项目 (No.QKJA201307)

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

XU Shan-ding1,2, CAO Xi-wang2,3, XU Guang-kui2,4   

  1. 1. Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing, Jiangsu 211167, China;
    2. School of Mathematical Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 211106, China;
    3. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China;
    4. School of Mathematical Science, Huainan Normal University, Huainan, Anhui 232038, China
  • Received:2014-10-10 Revised:2015-02-04 Online:2015-10-25 Published:2015-10-25

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.

关键词: 分圆, 跳频序列, 汉明相关, Lempel-Greenberger界, Peng-Fan界

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.

Key words: cyclotomy, frequency-hopping sequence, Hamming correlation, Lempel-Greenberger bound, Peng-Fan bound

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