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Introduction to Finite Fields and Their Applications. 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.
Polynomials over Finite Fields. Factorization of Polynomials. Exponential Sums. Linear Recurring Sequences. Theoretical Applications of Finite Fields. Algebraic Coding Theory. List of Symbols. Structure of Finite Fields. Harald Niederreiter.