Introduction to Finite Fields and their Applications

Presents an introduction to the theory of finite fields and some of its most important applications.

Rudolf Lidl (Author), Harald Niederreiter (Author)

9780521460941, Cambridge University Press

Hardback, published 21 July 1994

432 pages, 12 b/w illus. 6 tables 500 exercises
23.5 x 15.8 x 3.2 cm, 0.8 kg

' … a very useful and highly readable introduction to the classical theory and the standard applications of finite fields. It has a clear and precise presentation with many examples and a large selection of exercises.' The Mathematical Gazette

The theory of finite fields is a branch of modern algebra that has come to the fore in recent years because of its diverse applications in such areas as combinatorics, coding theory, cryptology and the mathematical study of switching circuits. The first part of this updated edition presents an introduction to this theory, emphasising those aspects that are relevant for application. The second part is devoted to a discussion of the most important applications of finite fields, especially to information theory, algebraic coding theory and cryptology. There is also a chapter on applications within mathematics, such as finite geometries, combinatorics and pseudo-random sequences. The book is meant to be used as a textbook: worked examples and copious exercises that range from the routine, to those giving alternative proofs of key theorems, to extensions of material covered in the text, are provided throughout. It will appeal to advanced undergraduates and graduate students taking courses on topics in algebra, whether they have backgrounds in mathematics, electrical engineering or computer science. Non-specialists will also find this a readily accessible introduction to an active and increasingly important subject.

1. Algebraic foundations
2. Structure of finite fields
3. Polynomials over finite fields
4. Factorization of polynomials
5. Exponential sums
6. Linear recurring sequences
7. Theoretical applications of finite fields
8. Algebraic coding theory
9. Cryptology
10. Tables.

Subject Areas: Algebra [PBF]