本文關(guān)鍵詞： 零差平衡函數(shù) 準(zhǔn)零差平衡函數(shù) 可劃分差族 可劃分幾乎差族　出處：《河北師范大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：丁存生在2008年為研究常重復(fù)合碼提出了一種新類型的組合函數(shù)—零差平衡函數(shù).零差平衡函數(shù)被廣泛應(yīng)用于編碼理論和通信領(lǐng)域中.它除了可用于構(gòu)作常重復(fù)合碼外,還可用于構(gòu)作跳頻序列、集合差系統(tǒng)等.準(zhǔn)零差平衡函數(shù)被視為零差平衡函數(shù)的自然推廣,是殷劍興、阿克俊在2014年提出的.準(zhǔn)零差平衡函數(shù)也可用于構(gòu)作常重復(fù)合碼、跳頻序列、集合差系統(tǒng)等,且具有更大的靈活性.本文主要研究準(zhǔn)零差平衡函數(shù)的組合構(gòu)作問題.基于有限域中的分圓理論并結(jié)合組合設(shè)計中有關(guān)差集、幾乎差集、差族、幾乎差族以及可劃分差族等理論的相關(guān)結(jié)論,給出準(zhǔn)零差平衡函數(shù)的若干新的遞歸構(gòu)作,同時還給出了一些直接構(gòu)作.本論文第一章介紹了一些相關(guān)概念及準(zhǔn)零差平衡函數(shù)的組合特性.第二章利用直接和遞歸的構(gòu)作方法給出了可劃分幾乎差族的若干無窮類.第三章我們研究一類特殊的準(zhǔn)零差平衡函數(shù)及其對應(yīng)的特殊的可劃分幾乎差族,基于兩者之間的等價關(guān)系,我們構(gòu)作出更多準(zhǔn)零差平衡函數(shù)的無窮類.最后討論了準(zhǔn)零差平衡函數(shù)的應(yīng)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
【學(xué)位授予單位】：河北師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O157.4

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