Table of contents for Error-correcting codes and finite fields / Oliver Pretzel.

Bibliographic record and links to related information available from the Library of Congress catalog

Information from electronic data provided by the publisher. May be incomplete or contain other coding.


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

Library of Congress subject headings for this publication:
Error-correcting codes (Information theory)