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ISBN 13: 9789390402236
Author: W B Vasantha Kandasamy, Florentin Smarandache, N Suresh Babu
Part I: The Fundamentals
Chapter 1: Preliminaries
1.1 Basic Concepts of Linear Algebra
1.1.1 Vector Spaces
1.1.2 Linear Maps
1.1.3 Bilinear Forms
1.1.4 Tensor Products
1.2 Finite Fields
1.3 Some Topics in Coding Theory
1.3.1 Linear Codes
1.3.2 Duality
1.3.3 The Singleton Bound
1.3.4 The Gilbert-Varshamov Bound
Chapter 2: Rank Distance Codes
2.1 Basic Definitions
2.2 Properties of Rank Distance Codes
2.3 The Singleton Bound for Rank Distance Codes
2.4 The Duality of Rank Distance Codes
2.5 Construction of Rank Distance Codes
2.6 Decoding of Rank Distance Codes
Part II: Rank Distance Bicodes
Chapter 3: Introduction to Rank Distance Bicodes
3.1 Basic Definitions
3.2 The Singleton Bound for Rank Distance Bicodes
3.3 The Duality of Rank Distance Bicodes
3.4 Constructions of Rank Distance Bicodes
Chapter 4: The Decoding of Rank Distance Bicodes
4.1 The Decoding Problem
4.2 A Decoding Algorithm for Rank Distance Bicodes
4.3 Performance Analysis
4.4 Applications of Rank Distance Bicodes
Part III: Generalizations and Future Research
Chapter 5: Generalizations of Rank Distance Bicodes
5.1 Introduction
5.2 Rank Distance Tricodes
5.3 Rank Distance m-Codes
5.4 Properties of Rank Distance m-Codes
5.5 Bounds for Rank Distance m-Codes
Chapter 6: Future Research Directions
6.1 Applications in Cryptography
6.2 Connections to Network Coding
6.3 Open Problems and Challenges
rank distance bicodes and their generalization
rank distance
distance rank algorithm
random distance generator
generalization of distance
Tags: W B Vasantha Kandasamy, Florentin Smarandache, N Suresh Babu, Rank, Bicodes