Coding Theory: A First Course

By Chaoping Xing

Coding Theory: A First Course

With numerous examples and exercises, this book contains a detailed and rigorous introduction to the theory of block codes and moves on to more advanced topics like BCH codes, Goppa codes and Sudan's algorithm for list decoding.

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Table of Contents

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Coding Theory A First Course

Chapter 1: Introduction

Chapter 2: Error Detection, Correction and Decoding

Chapter 3: Finite Fields

Chapter 4: Linear Codes

4.2: Linear Codes

4.3: Hamming Weight

4.4: Bases for Linear Codes

4.5: Generator Matrix and Parity-Check Matrix

4.6: Equivalence of Linear Codes

4.7: Encoding with a Linear Code

4.8: Decoding of Linear Codes

Exercises

Chapter 5: Bounds in Coding Theory

Chapter 6: Constructions of Linear Codes

Chapter 7: Cyclic Codes

Chapter 8: Some Special Cyclic Codes

Chapter 9: Goppa Codes

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