准零差平衡函数的组合构作

发布时间：2018-02-26 12:57

本文关键词： 零差平衡函数准零差平衡函数可划分差族可划分几乎差族　出处：《河北师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：丁存生在2008年为研究常重复合码提出了一种新类型的组合函数—零差平衡函数.零差平衡函数被广泛应用于编码理论和通信领域中.它除了可用于构作常重复合码外,还可用于构作跳频序列、集合差系统等.准零差平衡函数被视为零差平衡函数的自然推广,是殷剑兴、阿克俊在2014年提出的.准零差平衡函数也可用于构作常重复合码、跳频序列、集合差系统等,且具有更大的灵活性.本文主要研究准零差平衡函数的组合构作问题.基于有限域中的分圆理论并结合组合设计中有关差集、几乎差集、差族、几乎差族以及可划分差族等理论的相关结论,给出准零差平衡函数的若干新的递归构作,同时还给出了一些直接构作.本论文第一章介绍了一些相关概念及准零差平衡函数的组合特性.第二章利用直接和递归的构作方法给出了可划分几乎差族的若干无穷类.第三章我们研究一类特殊的准零差平衡函数及其对应的特殊的可划分几乎差族,基于两者之间的等价关系,我们构作出更多准零差平衡函数的无穷类.最后讨论了准零差平衡函数的应用.
[Abstract]:In 2008, Ding Cunsheng proposed a new type of combinational function called homodyne balance function for the study of constant repetition codes. The homodyne balance function is widely used in coding theory and communication fields. It can also be used to construct frequency hopping sequences, set difference systems, etc. The quasi homodyne balance function is regarded as a natural generalization of the homodyne balance function, which was put forward by Yin Jianxing and Arcajun in 2014. The quasi homodyne balance function can also be used to construct constant repeat codes. Frequency hopping sequence, set difference system and so on have more flexibility. In this paper, we mainly study the combinatorial construction of quasi homodyne balance function. Based on the theory of circle division in finite domain and combining with some difference sets, almost difference sets, differential families in combinatorial design, Some new recursive constructions of quasi-homodyne equilibrium function are given in this paper, which are related to the theory of almost difference family and divisible difference family. At the same time, some direct constructions are given. In the first chapter of this paper, we introduce some related concepts and the combinatorial properties of quasi-homodyne balance function. In chapter 2, by using the direct and recursive construction method, we give some kinds of partitioned almost differential families. In Chapter 3, we study a class of special quasi-homodyne equilibrium functions and their corresponding special separable almost differential families. Based on the equivalence relationship between them, we construct more infinite classes of quasi-homodyne balance functions. Finally, we discuss the application of quasi-homodyne balance functions
【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】：O157.4

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