Ferrers图秩度量码的构造

发布时间：2018-06-09 01:08

本文选题：Ferrers图 + 秩度量码　；参考：《苏州大学》2016年硕士论文

【摘要】：子空间码可用于随机网络编码,其存在性是近年来编码理论中的一个热点问题.常维数码作为一类特殊而重要的子空间码越来越受到人们的重视.多重构造方法作为构造常维数码的一种主要方法,它主要依赖于skeleton码的选择以及对应的Ferrers图秩度量码的存在性.本文第二章主要给出了两种构作Ferrers图秩度量码的方法,利用点膨胀和最大距离可分码填充的方法以及通过对小的Ferrers图进行适当组合的方法,得到大的Ferrers图秩度量码.并且利用这两种构作方法改进了几类Ferrers图秩度量码的下界,其中一类Ferrers图秩度量码的维数达到了最优.第三章主要通过改进多重构造方法中skeleton码的选择,给出了改进后的多重构造方法,并且利用此方法改进了几个常维数码的下界.
[Abstract]:Subspace codes can be used in random network coding. The existence of subspace codes is a hot issue in coding theory in recent years. As a special and important subspace code, the constant dimension code has been paid more and more attention. As a main method of constructing constant dimensional codes, multiplex construction mainly depends on the selection of skeleton codes and the existence of corresponding rank metric codes of Ferrers graphs. In the second chapter, we give two methods to construct rank metric codes of Ferrers graphs. By using the methods of point expansion, maximum distance divisible code filling and proper combination of small Ferrers graphs, we obtain large rank metric codes of Ferrers graphs. The lower bounds of several kinds of rank metric codes of Ferrers graphs are improved by using these two methods, in which the dimension of rank metric codes of a class of Ferrers graphs is optimal. In chapter 3, the improved multiplex construction method is presented by the selection of skeleton codes in the improved multiplex construction method, and the lower bounds of several constant dimensional codes are improved by this method.
【学位授予单位】：苏州大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O157.4

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