Mathematics and Statistics Faculty and Staff Publications

Book

2012

Abstract

In this book the authors study the erasure techniques in concatenated Maximum Rank Distance (MRD) codes. The authors for the first time in this book introduce the new notion of concatenation of MRD codes with binary codes, where we take the outer code as the RD code and the binary code as the inner code. The concatenated code consists of the codewords of the outer code expressed in terms of the alphabets of the inner code. These new class of codes are defined as CRM codes. This concatenation techniques helps one to construct any CRM code of desired minimum distance which is not enjoyed by any other class of codes. Also concatenation of several binary codes are introduced using the newly defined notion of special blanks. These codes can be used in bulk transmission of a message into several channels and the completed work is again consolidated and received. Finally the notion of integer rank distance code is introduced. This book is organized into six chapters. The first chapter introduces the basic algebraic structures essential to make this book a self contained one. Algebraic linear codes and their basic properties are discussed in chapter two. In chapter three the authors study the basic properties of erasure decoding in maximum rank distance codes. Some decoding techniques about MRD codes are described and discussed in chapter four of this book.

Publisher

Zip Publishing, Ohio

ISSN

978-1-59973-177-3

English

Keywords

decoding techniques, erasure techniques, Maximum Rank Distance, MRD

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