Error-Correcting Codes and Finite Fields / Edition 1

Error-Correcting Codes and Finite Fields / Edition 1

by Oliver Pretzel
     
 

ISBN-10: 0192690671

ISBN-13: 9780192690678

Pub. Date: 08/28/1996

Publisher: Oxford University Press, USA

This book provides engineers and computer scientists with all the tools necessary to implement modern error-processing techniques. It assumes only a basic knowledge of linear algebra and develops the mathematical theory in parallel with the codes. Central to the text are worked examples which motivate and explain the theory. The first part introduces the basic

Overview

This book provides engineers and computer scientists with all the tools necessary to implement modern error-processing techniques. It assumes only a basic knowledge of linear algebra and develops the mathematical theory in parallel with the codes. Central to the text are worked examples which motivate and explain the theory. The first part introduces the basic ideas of coding theory. The second and third cover the theory of finite fields and give a detailed treatment of BCH and Reed-Solomon codes. The fourth part is devoted to Goppa codes, both classical and geometric, concluding with the Skorobogatov-Vladut error processor. A special feature is a simplified (but rigorous) treatment of the geometry of curves.

Product Details

ISBN-13:
9780192690678
Publisher:
Oxford University Press, USA
Publication date:
08/28/1996
Series:
Oxford Applied Mathematics and Computing Science Series
Edition description:
Student Edition
Pages:
360
Product dimensions:
9.13(w) x 6.13(h) x 0.79(d)

Table of Contents

PART I: Basic Coding Theory
1. Introduction
2. Block Codes, Weight, and Distance
3. Linear Codes
4. Error Processing for Linear Codes
5. Hamming Codes and the Binary Golay Codes
PART II: Finite Fields
6. Introduction
7. Euclid's Algorithm
8. Invertible and Irreducible Elements
9. The Construction of Finite Fields
10. The Structure of Finite Fields
11. Roots of Polynomials
12. Primitive Elements
PART III: BCH and Other Cyclic Codes
13. BCH Codes as Subcodes of Hamming Codes
14. BCH Codes as Polynomial Codes
15. Decoding BCH Codes: The Fundamental Equation
16. Decoding BCH Codes: A Decoding Algorithm
17. Reed-Solomon Codes and Burst Error Correction
18. Bounds on Codes
PART IV: Classical and Geometric Goppa Codes
19. Classical Goppa Codes
20. Classical Goppa Codes: Error Processing
21. Introduction to Algebraic Curves
22. Functions on Algebraic Curves
23. A Survey of the Theory of Algebraic Curves
24. Geometric Goppa Codes
25. An Error Processor for Geometric Goppa Codes

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