This book provides a brief and accessible introduction to the theory of finite fields and to a couple 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 and every 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 variety of constructions and basic properties of error-correcting codes and cryptographic systems the use of finite fields. Each and every chapter includes a set of exercises of varying levels of difficulty which lend a hand to further give an explanation for and motivate the material. Appendix A provides a brief review of the basic number theory and abstract algebra used in the text, in addition to exercises related to this material. Appendix B provides hints and partial solutions for a few of the exercises in Each and every chapter. A list of 64 references to further reading and to additional topics related to the book’s material could also be included. Intended for advanced undergraduate students, it’s suitable both for classroom use and for individual study. This book is co-published with Mathematics Advanced Study Semesters.
Finite Fields and Applications (Student Mathematical Library)