Coding Theory A First Course

Concerned with successfully transmitting data through a noisy channel, coding theory can be applied to electronic engineering and communications. Based on the authors' extensive teaching experience, this text provides a completely modern and accessible course on the subject. It includes sections on linear programming and decoding methods essential for contemporary mathematics. Numerous examples and exercises make the volume ideal for students and instructors.

Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. It 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. The issues of bounds and decoding, essential to the design of good codes, features prominently. The authors of this book have, for several years, successfully taught a course on coding theory to students at the National University of Singapore. This book is based on their experiences and provides a thoroughly modern introduction to the subject. There are numerous examples and exercises, some of which introduce students to novel or more advanced material.

1. Introduction; 2. Error detection, correction and decoding; 3. Finite fields; 4. Linear codes; 5. Bounds in coding theory; 6. Constructions of linear codes; 7. Cyclic codes; 8. Some special cyclic codes; 9. Goppa codes.

Based on the authors' teaching experiences, this book provides a thoroughly modern introduction to the coding theory - a subject of central importance for many applications in engineering and computer science. There are numerous examples and exercises, some of which introduce students to novel or more advanced material.