Codes and Curves (Student Mathematical Library, Vol. 7)

Have nothing glowing to say about this book.

The book gives an overview of algebraic coding theory. The first chapter introduces error correcting codes, the Hamming distance, Reed-Solomon codes, and concludes with a brief exposition of cyclic codes. The second chapter discusses some upper bounds on the minimum distance of a code such as the Singleton and Plotkin bounds.The second theme of this book are algebraic curves. Chapter 3 contains the basic definitions and some examples of algebraic curves. The concept of a nonsingular curve is explained in Chapter 4. This chapter also contains a half page explanation of the genus of a curve. The Riemann-Roch theorem is finally covered in Chapter 5.The two themes come together in Chapters 6 and 7. These chapters discuss the basic principles of algebraic geometry codes.This little book gives the reader a first taste of an intriguing field. The most surprising part is how much is covered in so few pages [the main text without appendices has 44 pages]. The explanations are always accessible for undergraduate students of mathematics, computer science, or electrical engineering. The prerequisites are some knowledge of abstract algebra, but most material is reviewed in the appendices.It is a lovely little book that is written in a lively style. The book nicely complements the typical college courses on coding theory. If you want to get an idea what algebraic geometric codes are and you want a quick answer, then this is the book for you.

There is a free version of the book available on the website of the University of Nebraska-Lincoln.