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Erasure Techniques in MRD Codes

By Smarandache, Florentin

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Book Id: WPLBN0002828250
Format Type: PDF (eBook)
File Size: 3.11 mb
Reproduction Date: 7/18/2013

Title: Erasure Techniques in MRD Codes  
Author: Smarandache, Florentin
Language: English
Subject: Non Fiction, Education, Algebra
Collections: Mathematics, Algebra, Technology, Arithmetic, Authors Community, Math, Fine Arts, Literature, Most Popular Books in China, Favorites in India, Education, Law
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Publisher: World Public Library
Member Page: Florentin Smarandache


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Smarandache, F., & Vasantha Kandasamy, W. B. (2013). Erasure Techniques in MRD Codes. Retrieved from

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.

We want to find efficient algebraic methods to improve the realiability of the transmission of messages. In this chapter we give only simple coding and decoding algorithms which can be easily understood by a beginner. Binary symmetric channel is an illustration of a model for a transmission channel. Now we will proceed onto define a linear code algebraically.

Table of Contents
Preface 5 Chapter One BASIC CONCEPTS 7 Chapter Two ALGEBRAIC LINEAR CODES AND THEIR PROPERTIES 29 Chapter Three ERASURE DECODING OF MAXIMUM RANK DISTANCE CODES 49 3.1 Introduction 49 3.2 Maximum Rank Distance Codes 51 3.3 Erasure Decoding of MRD Codes 54 Chapter Four MRD CODES –SOME PROPERTIES AND A DECODING TECHNIQUE 63 4.1 Introduction 63 4.2 Error-erasure Decoding Techniques to MRD Codes 64 4.3 Invertible q-Cyclic RD Codes 83 4.4 Rank Distance Codes With Complementary Duals 101 4.4.1 MRD Codes With Complementary Duals 103 4.4.2 The 2-User F-Adder Channel 106 4.4.3 Coding for the 2-user F-Adder Channel 107 Chapter Five EFFECTIVE ERASURE CODES FOR RELIABLE COMPUTER COMMUNICATION PROTOCOLS USING CODES OVER ARBITRARY RINGS 111 5.1 Integer Rank Distance Codes 112 5.2 Maximum Integer Rank Distance Codes 114 Chapter Six CONCATENATION OF ALGEBRAIC CODES 129 6.1 Concatenation of Linear Block Codes 129 6.2 Concatenation of RD Codes With CR-Metric 140 FURTHER READING 153 INDEX 157 ABOUT THE AUTHORS 161


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