一类最优跳频序列族的代数构造

doi:10.12341/jssms12870

系统科学与数学 ›› 2016, Vol. 36 ›› Issue (8): 1329-1338.DOI: 10.12341/jssms12870

一类最优跳频序列族的代数构造

徐善顶¹，曹喜望²，许广魁³

1.南京工程学院数理部,南京 211167; 南京航空航天大学数学系,南京 211106;2.南京航空航天大学数学系, 南京 211106; 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;3.南京航空航天大学数学系,南京 211106; 淮南师范学院数学系,淮南 232038

出版日期:2016-08-25 发布日期:2016-09-26

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徐善顶，曹喜望，许广魁. 一类最优跳频序列族的代数构造[J]. 系统科学与数学, 2016, 36(8): 1329-1338.

XU Shanding,CAO Xiwang,XU Guangkui. AN ALGEBRAIC CONSTRUCTION OF OPTIMAL FREQUENCY-HOPPING SEQUENCES SET[J]. Journal of Systems Science and Mathematical Sciences, 2016, 36(8): 1329-1338.

AN ALGEBRAIC CONSTRUCTION OF OPTIMAL FREQUENCY-HOPPING SEQUENCES SET

XU Shanding ¹, CAO Xiwang², XU Guangkui³

1.Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167; Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106;2.Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016;State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093;3.Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106;Department of Mathematics, Huainan Normal University, Huainan 232038

Online:2016-08-25 Published:2016-09-26

在通信系统中, 直接序列扩频和跳频扩频是两种最主要的扩散编码技术. 而在FH-CDMA系统中, 跳频序列被广泛使用. 利用分圆法和离散对数函数, 首先构造了一类具有新参数的跳频序列族, 并给出了各类汉明相关值的计算公式. 其次, 证明了所构造的跳频序列(族)所具有的最优性.

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

Direct-sequence spread spectrum and frequency-hopping spread spectrum are two main spread coding technologies in communication systems. Frequency-hopping sequences are widely needed in FH-CDMA systems. Firstly, a new frequency-hopping sequences set with new parameters is constructed, the calculation formulas of all kinds of Hamming correlation values of which are given. Secondly, the proposed frequency-hopping sequences (set) are shown to be optimal.

MR(2010)主题分类:

94A55

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