ABSTRACT

This book is designed to be usable as a textbook for an undergraduate course or for an advanced graduate course in coding theory as well as a reference for researchers in discrete mathematics, engineering and theoretical computer science. This second edition has three parts: an elementary introduction to coding, theory and applications of codes, and algebraic curves. The latter part presents a brief introduction to the theory of algebraic curves and its most important applications to coding theory.

part I|132 pages

An elementary introduction to coding

chapter 1|19 pages

The concept of coding

chapter 2|18 pages

Binary linear codes

chapter 3|29 pages

General linear codes

chapter 4|10 pages

Singleton bound and Reed-Solomon codes

chapter 5|11 pages

Recursive constructions I

chapter 6|4 pages

Universal hashing

chapter 7|4 pages

Designs and the binary Golay code

chapter 9|12 pages

Asymptotic results

chapter 11|2 pages

Summary and outlook

part II|261 pages

Theory and applications of codes

chapter 12|16 pages

Subfield codes and trace codes

chapter 13|38 pages

Cyclic codes

chapter 15|34 pages

The linear programming method

chapter 17|64 pages

The geometric description of linear codes

chapter 18|45 pages

Additive codes and network codes

part III|91 pages

Codes and algebraic curves

chapter 19|7 pages

Introduction

chapter 20|16 pages

Function fields, their places and valuations

chapter 21|9 pages

Determining the genus

chapter 23|39 pages

The last chapter