Constructions Of Ferrers Diagram Rank-Metric Codes

In 2000,Ahlswede et al.Broke through the previous tradition and allowed the intermediate nodes to process the data in the network communication,thus proposed the concept of network coding.Compared with the traditional routing network,network coding has many advantages in throughput,security,transmission energy consumption and so on.Therefore,it is highly concerned by scholars all over the world and is considered as the core technology of the future network.In 2008,koetter and kschischang proposed an important research content of network error correction coding in incoherent network environment,subspace code,and studied a special and important subspace code,constant dimension code,which has attracted widespread attention.In 2009,Etzion and Silberstein proposed the method of constructing constant dimensional codes by multilevel construction.In this method,we need to construct a matrix code called Ferrers diagram rank-metric code.Ferrers diagram rank-metric code is an important auxiliary code for constructing constant dimension code,which plays a key role in multilevel construction.This article mainly studies the constructions of Ferrers diagram rank-metric codes.The organization structure of the article is as follows: Chapter 1 introduces the basic knowledge related to this article;Chapter 2 lists the currently known constructions of Ferrers diagram rank-metric codes;In Chapter 3,the main results of this article are given;the last chapter summarizes the main content of this article and puts forward some questions that can be further studied.In the constructions of the Ferrers diagram rank-metric codes,this article mainly has the following three results:First,in the method of constructing the Ferrers diagram rank-metric codes proposed by Shuangqing Liu and others(Lemma 3.1.2),it is necessary to construct a coefficient matrix that satisfies certain conditions,but there has been no general method for constructing such a coefficient matrix.We have studied the property of Extended RS code,transform it,and give a general method for constructing this kind of coefficient matrix.Second,we referred to Shuangqing Liu et al.’s method of using MRD codes to take sub-codes to construct Ferrers diagram rank-metric codes(Construction 3.1.3),and tried to extend this method.Finally,by constructing a new generation matrix of MRD codes,we obtained a new class of Ferrers diagram rank-metric codes.The newly constructed Ferrers diagram rank-metric codes cannot be obtained by other currently known methods.Third,in the construction method of MRD code sub-code,if the MRD code generation matrix has only two rows,then another different MRD code generation matrix can be constructed.Through this MRD code generation matrix,you can also get other new Ferrers graph rank metric code classes.