Introduction to Finite Fields and their Applications
Seiten
1994
|
2nd Revised edition
Cambridge University Press (Verlag)
978-0-521-46094-1 (ISBN)
Cambridge University Press (Verlag)
978-0-521-46094-1 (ISBN)
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. This book presents an introduction to this theory, and contains a discussion of the most important applications of finite fields.
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 updated edition presents an introduction to this theory, emphasising 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 meant to be used as a 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. It will appeal to advanced undergraduates and graduate students taking courses on topics in algebra, whether they have backgrounds in mathematics, electrical engineering or computer science. Non-specialists will also find this a readily accessible introduction to an active and increasingly important subject.
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 updated edition presents an introduction to this theory, emphasising 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 meant to be used as a 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. It will appeal to advanced undergraduates and graduate students taking courses on topics in algebra, whether they have backgrounds in mathematics, electrical engineering or computer science. Non-specialists will also find this a readily accessible introduction to an active and increasingly important subject.
1. Algebraic foundations; 2. Structure of finite fields; 3. Polynomials over finite fields; 4. Factorization of polynomials; 5. Exponential sums; 6. Linear recurring sequences; 7. Theoretical applications of finite fields; 8. Algebraic coding theory; 9. Cryptology; 10. Tables.
| Erscheint lt. Verlag | 21.7.1994 |
|---|---|
| Zusatzinfo | Worked examples or Exercises; 6 Tables, unspecified; 12 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 158 x 235 mm |
| Gewicht | 800 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 0-521-46094-8 / 0521460948 |
| ISBN-13 | 978-0-521-46094-1 / 9780521460941 |
| Zustand | Neuware |
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