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Rank Distance Bicodes and Their Generalization

By Smarandache, Florentin

Book Id: WPLBN0002828550
Format Type: PDF (eBook)
File Size: 2.57 mb
Reproduction Date: 8/7/2013

Title:	Rank Distance Bicodes and Their Generalization
Author:	Smarandache, Florentin
Volume:
Language:	English
Subject:	Non Fiction, Education, Bicodes
Collections:	Mathematics, Authors Community
Historic Publication Date:	2013
Publisher:	World Public Library

Member Page:	Florentin Smarandache
Citation APA MLA Chicago Smarandache, F., & Vasantha Kandasamy, W. B. (2013). Rank Distance Bicodes and Their Generalization. Retrieved from http://self.gutenberg.org/

Description
This book has four chapters. In chapter one we just recall the notion of RD codes, MRD codes, circulant rank codes and constant rank codes and describe their properties. In chapter two we introduce few new classes of codes and study some of their properties. In this chapter we introduce the notion of fuzzy RD codes and fuzzy RD bicodes. Rank distance m-codes are introduced in chapter three and the property of m-covering radius is analysed. Chapter four indicates some applications of these new classes of codes.

Summary
In this book the authors introduce the new notion of rank distance bicodes and generalize this concept to Rank Distance n-codes (RD n-codes), n, greater than or equal to three. This definition leads to several classes of new RD bicodes like semi circulant rank bicodes of type I and II, semicyclic circulant rank bicode, circulant rank bicodes, bidivisible bicode and so on. It is important to mention that these new classes of codes will not only multitask simultaneously but also they will be best suited to the present computerised era. Apart from this, these codes are best suited in cryptography.

Excerpt
DEFINITION 1.12: The ‘norm’ of a word v _ VN is defined as the ‘rank’ of v over GF(2) (By considering it as a circulant matrix over GF(2)). We denote the ‘norm’ of v by r(v). We just prove the following theorem. THEOREM 1.2: Suppose ____GF(2N) has the polynomial representation g(x) over GF(2) such that the gcd(g(x), xN +1) has degree N – k, where 0 _ k _ N. Then the ‘norm’ of the word generated by _ is ‘k’.

Table of Contents
Preface 5 Chapter One BASIC PROPERTIES OF RANK DISTANCE CODES 7 Chapter Two RANK DISTANCE BICODES AND THEIR PROPERTIES 25 Chapter Three RANK DISTANCE m-CODES 77 Chapter Four APPLICATIONS OF RANK DISTANCE m-CODES 131 FURTHER READING 133 INDEX 144 ABOUT THE AUTHORS 150