Introduction to Finite Fields and their Applications

by Rudolf Lidl, Harald Niederreiter

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 book presents an introduction to this theory, emphasizing 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 designed as a graduate level 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.

432 pages, Hardcover

First published July 21, 1994

Reviews

[Jake · Rating 4 out of 5]

I only read the first chapter, Algebraic Foundations, as a precursor to Dummit & Foote's treatment of Galois theory. Well-written with excellent exercises, really allows students to hit the ground running.

[Review #1 - 30/08/23.]