零差平衡函数的组合构作

发布时间：2018-01-02 06:04

本文关键词：零差平衡函数的组合构作　出处：《河北师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：零差平衡函数(zero-difference balanced functions)是由丁存生在研究常重复合码时定义的一种组合结构.常重复合码是在通信工程领域中为研究平衡调度和电力传输而提出的一类特殊的常重码.它广泛的应用于多址通信系统、编码、跳频序列和球码调制等方面.零差平衡函数还可用来构作集合差系统.集合差系统是由Levenstein在构作无逗码时定义的组合结构.2008年,丁存生利用有限域上的迹函数构作了一类零差平衡函数.2012年,周正春等人利用差平衡函数给出了两类零差平衡函数的一般构作.2013年,蔡晗等人利用广义分圆类构作了一类新的零差平衡函数.2014年,Q.Wang等人给出了零差平衡函数的一般构作.同年,丁存生等人构作了三类新的零差平衡函数.2015年,查正邦等人给出了零差平衡函数的若干分圆构作.丁存生等人指出了零差平衡函数和可划分差族的等价关系.可划分差族最早是由丁存生和殷剑兴在研究常重复合码时定义的.殷剑兴,王金华等人利用有限域分圆理论构作了若干类的可划分差族.王成敏等人给出了用1-rotational可分解的平衡不完全区组设计构作可划分差族的方法.朱坤利用分圆类的拆分和整合,也给出了若干类的可划分差族.本文第一章介绍相关的概念和结论.第二章从可划分差族入手,给出若干类新的零差平衡函数.第三章分别介绍零差平衡函数在最优常重复合码、完美集合差系统和跳频序列上的应用.
[Abstract]:Zero difference balance function (zero-difference balanced functions) is a kind of composite structure defined by Ding Cunsheng in the study of constant composition codes. Constant composition codes is proposed for the study of balanced scheduling and power transmission in the field of communication engineering in a special class of constant weight codes. It is widely used in multiple access communication system. Encoding, aspects of frequency hopping sequences and ball code modulation. Zero differential equilibrium functions can also be used to construct the set differential system. Difference system of sets is defined by Levenstein in the construction of the composite structure without make code.2008, using the Ding Cunsheng trace function over finite fields to construct a class of zero difference balance function.2012 years. Zhou Zhengchun et al use difference balance are given two kinds of function zero difference balance function for the general construction of.2013 years, Cai Han et al. By using the generalized cyclotomic class to construct a new class of zero difference balance function in.2014, Q.Wang et al proposed zero difference balance function The general structure of the number. The same year, Ding Cunsheng et al to construct three new zero difference balance function in.2015, the number of Cyclotomic homodyne balanced function to construct bond et al. Ding Cunsheng et al are found out and can be divided into zero difference balanced function difference family equivalence relation can be divided. The first difference family is defined by Ding Cunsheng and Yin Jianxing in the study of constant composition codes. Yin Jianxing, Wang Jinhua, et al. Using finite field theory to construct a number of Cyclotomic classes can be divided into poor family. Wang Chengmin et al is presented by the 1-rotational decomposition of the balanced incomplete block design construction method can be divided into difference families. The use of Zhu Kun round type separation and integration are also given some kind of divided difference family. The first chapter introduces the related concepts and conclusions. The second chapter starts from the divided difference family, given some new classes of homodyne balanced function. The third chapter introduces the zero difference balance function The application of the number in the optimal constant repeating code, the perfect set difference system and the frequency hopping sequence.

【学位授予单位】：河北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O156

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