Finite Fields and Applications
About this Title
Gary L. Mullen, Pennsylvania State University, University Park, PA and Carl Mummert, University of Michigan, Ann Arbor, MI
Publication: The Student Mathematical Library
Publication Year 2007: Volume 41
ISBNs: 978-0-8218-4418-2 (print); 978-1-4704-2150-2 (online)
MathSciNet review: MR2358760
MSC: Primary 05-01; Secondary 05B15, 11T71, 12E20, 94A60, 94Bxx
This book provides a brief and accessible introduction to the theory of finite fields and to some of their many fascinating and practical applications.
The first chapter is devoted to the theory of finite fields. After covering their construction and elementary properties, the authors discuss the trace and norm functions, bases for finite fields, and properties of polynomials over finite fields.
Each of the remaining chapters details applications. Chapter 2 deals with combinatorial topics such as the construction of sets of orthogonal latin squares, affine and projective planes, block designs, and Hadamard matrices. Chapters 3 and 4 provide a number of constructions and basic properties of error-correcting codes and cryptographic systems using finite fields.
Each chapter includes a set of exercises of varying levels of difficulty which help to further explain and motivate the material. Appendix A provides a brief review of the basic number theory and abstract algebra used in the text, as well as exercises related to this material. Appendix B provides hints and partial solutions for many of the exercises in each chapter. A list of 64 references to further reading and to additional topics related to the book's material is also included.
Intended for advanced undergraduate students, it is suitable both for classroom use and for individual study.
Undergraduate and graduate students interested in the theory of finite fields and applications.
Table of Contents
- Chapter 1. Finite fields
- Chapter 2. Combinatorics
- Chapter 3. Algebraic coding theory
- Chapter 4. Cryptography
- Appendix A. Background in number theory and abstract algebra
- Appendix B. Hints for selected exercises