The theory of finite fields is a branch of algebra that has come to the fore because of its diverse applications in such areas as combinatorics, coding theory and the mathematical study of switching ciruits. This book is devoted entirely to the theory of finite fields, and it provides comprehensive coverage of the literature. Bibliographical notes at the end of each chapter give an historical survey of the development of the subject. Worked-out examples and lists of exercises found throughout the book make it useful as a text for advanced-level courses.

• The classic book on finite fields • Second edition has been updated and corrected throughout • Authors very well known for their work in this area

### Contents

1. Algebraic foundations; 2. Structure of finite fields; 3. Polynomials over finite fields; 4. Factorization of polynomials; 5. Exponential sums; 6. Equations over finite fields; 7. Permutation polynomials; 8. Linear recurring sequences; 9. Applications of finite fields; 10. Tables.

### Reviews

Review of the hardback: 'This well-written treatise deserves attention from everyone interested in any of the several areas in which finite fields arise today.' SIAM Review

Review of the hardback: 'This book is devoted entirely to the theory of finite fields … it provides comprehensive coverage … useful as a text for advanced level courses.' L'Enseignement Mathématique

Review of the hardback: 'An excellent and self-contained book.' European Mathematical Society