The comments above explain why it seemed reasonable (to me) to translatethe Dutch book into English. In the name of Springer-Verlag I thank theMathematical Centre in Amsterdam for permission to do so.

Preface to the Third Edition

Preface to the Second Edition

Preface to the First Edition

CHAPTER 1 Mathematical Backblound

 1.1. Algebra

 1.2. Krawtchouk Polynomials

 1.3. Combinatorial Theory

 1.4. Probability Theory

CHAPTER 2 Shannon's Theorem

 2.1. Introduction

 2.2. Shannon's Theorem

 2.3. On Coding Gain

 2.4. Comments

 2.5. Problems

CHAPTER 3 Linear Codes

 3.1. Block Codes

 3.2. Linear Codes

 3.3. Hamming Codes

 3.4. Majority Logic Decoding

 3.5. Weight Enumerators

 3.6. The Lee Metric

 3.7. Comments

 3.8. Problems

CHAPTER 4 Some Good Codes

 4.1. Hadamard Codes and Generalizations

 4.2. The Binary Golay Code

 4.3. The Temary Golay Code

 4.4. Constructing Codes from Other Codes

 4.5. Reed-Muller Codes

 4.6. Kerdock Codes

 4.7. Comments

 4.8. Problems

CHAPTER 5 Bounds on Codes

 5.1. Introduction: The Gilbert Bound

 5.2. Upper Bounds

 5.3. The Linear Programming Bound

 5.4. Comments

 5.5. Problems

CHAPTER 6 Cyclic Codes

 6.1. Definitions

 6.2. Generator Matrix and Check Polynomial

 6.3. Zeros of a Cyclic Code

 6.4. The Idempotent of a Cyclic Code

 6.5. Other Representations of Cyclic Codes

 6.6. BCH Codes

 6.7. Decoding BCH Codes

 6.8. Reed-Solomon Codes

 6.9. Quadratic Residue Codes

 6.10. Binary Cyclic Codes of Length 2n(n odd)

 6.11. Generalized Reed-Muller Codes

 6.12. Comments

 6.13. Problems

CHAPTER 7 Perfect Codes and Uniformly Packed Codes

 7.1. Lloyd's Theorem

 7.2. The Characteristic Polynomial of a Codetents

 7.3. Uniformly Packed Codes

 7.4. Examples of Uniformly Packed Codes

 7.5. Nonexistence Theorems

 7.6. Comments

 7.7. Problems

CHAPTER 8 Codes over ■

 8.1. Quaternary Codes

 8.2. Binary Codes Derived from Codes over ■

 8.3. Galois Rings over ■

 8.4. Cyclic Codes over■

 8.5. Problems

CHAPTER 9 Goppa Codes

 9.1. Motivation

 9.2. Goppa Codes

 9.3. The Minimum Distance of Goppa Codes

 9.4. Asymptotic Behaviour of Goppa Codes

 9.5. Decoding Goppa Codes

 9.6. Generalized BCH Codes

 9.7. Comments

 9.8. Problems

CHAPTER I0 Algebraic Geometry Codes

 10.1. Introduction

 10.2. Algebraic Curves

 10.3. Divisors

 10.4. Differentials on a Curve

 10.5. The Riemann-Roch Theorem

 10.6. Codes from Algebraic Curves

 10.7. Some Geometric Codes

 10.8. Improvement of the Gilbert-Varshamov Bound

 10.9. Comments

 10.10. Problems

CHAPTER 11 Asymptotically Good Algebraic Codes

 11.1. A Simple Nonconstructive Example

 11.2. Justesen Codes

 11.3. Comments

 11.4. Problems

CHAPTER 12 Arithmetic Codes

 12.1. AN Codes

 12.2. The Arithmetic and Modular Weight

 12.3. Mandelbaum-Barrows Codes

 12.4. Comments

 12.5. Problems

CHAPTER 13 Convolutional Codes

 13.1. Introduction

 13.2. Decoding of Convolutional Codes

 13.3. An Analog of the Gilbert Bound for Some Convolutional Codes

 13.4. Construction of Convolutional Codes from Cyclic Block Codes

 13.5. Automorphisms of Convolutional Codes

 13.6. Comments

 13.7. Problems

Hints and Solutions to Problems

References

Index