Introduction to Coding Theory

✍ Scribed by J. H. van Lint (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1999
• Tongue: English
• Leaves: 243
• Series: Graduate Texts in Mathematics 86
• Edition: 3
• Category: Library

✦ Synopsis

It is gratifying that this textbook is still sufficiently popular to warrant a third edition. I have used the opportunity to improve and enlarge the book. When the second edition was prepared, only two pages on algebraic geometry codes were added. These have now been removed and replaced by a relatively long chapter on this subject. Although it is still only an introduction, the chapter requires more mathematical background of the reader than the remainder of this book. One of the very interesting recent developments concerns binary codes defined by using codes over the alphabet 7l.4• There is so much interest in this area that a chapter on the essentials was added. Knowledge of this chapter will allow the reader to study recent literature on 7l. -codes. 4 Furthermore, some material has been added that appeared in my Springer Lec­ ture Notes 201, but was not included in earlier editions of this book, e. g. Generalized Reed-Solomon Codes and Generalized Reed-Muller Codes. In Chapter 2, a section on "Coding Gain" ( the engineer's justification for using error-correcting codes) was added. For the author, preparing this third edition was a most welcome return to mathematics after seven years of administration. For valuable discussions on the new material, I thank C.P.l.M.Baggen, I. M.Duursma, H.D.L.Hollmann, H. C. A. van Tilborg, and R. M. Wilson. A special word of thanks to R. A. Pellikaan for his assistance with Chapter 10.

✦ Table of Contents

Front Matter....Pages I-XIV
Mathematical Background....Pages 1-21
Shannon’s Theorem....Pages 22-32
Linear Codes....Pages 33-46
Some Good Codes....Pages 47-63
Bounds on Codes....Pages 64-80
Cyclic Codes....Pages 81-111
Perfect Codes and Uniformly Packed Codes....Pages 112-127
Codes over ℤ 4 ....Pages 128-138
Goppa Codes....Pages 139-147
Algebraic Geometry Codes....Pages 148-166
Asymptotically Good Algebraic Codes....Pages 167-172
Arithmetic Codes....Pages 173-180
Convolutional Codes....Pages 181-194
Back Matter....Pages 195-233

✦ Subjects

Combinatorics; Algebraic Geometry; Number Theory