Finite Fields for Computer Scientists and Engineers - ISBN:0898381916

Finite Fields for Computer Scientists and Engineers

Date: 14 April 2011, 01:22

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The theory of finite fields is of central importance in engineering and computer science, because of its applications to error-correcting codes, cryptography, spread-spectrum communications, and digital signal processing. Though not inherently difficult, this subject is almost never taught in depth in mathematics courses, (and even when it is the emphasis is rarely on the practical aspect). Indeed, most students get a brief and superficial survey which is crammed into a course on error-correcting codes. It is the object of this text to remedy this situation by presenting a thorough introduction to the subject which is completely sound mathematically, yet emphasizes those aspects of the subject which have proved to be the most important for applications.
This book is unique in several respects. Throughout, the emphasis is on fields of characteristic 2, the fields on which almost all applications are based. The importance of Euclid's algorithm is stressed early and often. Berlekamp's polynomial factoring algorithm is given a complete explanation. The book contains the first treatment of Berlekamp's 1982 bit-serial multiplication circuits, and concludes with a thorough discussion of the theory of m-sequences, which are widely used in communications systems of many kinds.
Summary: Excellent introduction to coding theory
Rating: 5
I read this book as a learning tool to help my study of coding theory, and I find this book to be very well written and very helpful.
McEliece excuses himself for covering only what he considers the 'dry' part of finite fields, but the exercises in this book do a great job in giving examples of the more engineering applications of the theory presented in this book.
An interesting side note is that several of the graduate students listed in the preface are now well-known professors in digital communications, including Jim Lehnert at Purdue and Wayne Stark at Michigan.
Since this text is fairly old, this book is highly recommended as an introduction to coding theory based on classical constructions. To my knowledge there are no good textbooks published that covers graphical codes to this date (year 2000). If you are interested in graphical codes (such as LDPC or Turbo Codes), see McEliece's excellent "The Generalized Distributive Law" paper on the IEEE Transactions on Information Theory, March 2000.

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