Algebraic Geometric Codes: Basic Notions
Seiten
2007
American Mathematical Society (Verlag)
978-0-8218-4306-2 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-4306-2 (ISBN)
- Titel ist leider vergriffen;
keine Neuauflage - Artikel merken
Deals with the theory of algebraic geometric codes, a subject formed on the border of several domains of mathematics. This book looks for interpretations that connect coding theory to algebraic geometry and number theory. It pays attention to the geometry of curves over finite fields.
The book is devoted to the theory of algebraic geometric codes, a subject formed on the border of several domains of mathematics. On one side there are such classical areas as algebraic geometry and number theory; on the other, information transmission theory, combinatorics, finite geometries, dense packings, etc. The authors give a unique perspective on the subject. Whereas most books on coding theory build up coding theory from within, starting from elementary concepts and almost always finishing without reaching a certain depth, this book constantly looks for interpretations that connect coding theory to algebraic geometry and number theory. There are no prerequisites other than a standard algebra graduate course. The first two chapters of the book can serve as an introduction to coding theory and algebraic geometry respectively. Special attention is given to the geometry of curves over finite fields in the third chapter. Finally, in the last chapter the authors explain relations between all of these: the theory of algebraic geometric codes.
The book is devoted to the theory of algebraic geometric codes, a subject formed on the border of several domains of mathematics. On one side there are such classical areas as algebraic geometry and number theory; on the other, information transmission theory, combinatorics, finite geometries, dense packings, etc. The authors give a unique perspective on the subject. Whereas most books on coding theory build up coding theory from within, starting from elementary concepts and almost always finishing without reaching a certain depth, this book constantly looks for interpretations that connect coding theory to algebraic geometry and number theory. There are no prerequisites other than a standard algebra graduate course. The first two chapters of the book can serve as an introduction to coding theory and algebraic geometry respectively. Special attention is given to the geometry of curves over finite fields in the third chapter. Finally, in the last chapter the authors explain relations between all of these: the theory of algebraic geometric codes.
Codes Curves Curves over finite fields Algebraic geometry codes Summary of results and tables Bibliography List of names Index.
Erscheint lt. Verlag | 29.1.2008 |
---|---|
Reihe/Serie | Mathematical Surveys and Monographs |
Zusatzinfo | Illustrations |
Verlagsort | Providence |
Sprache | englisch |
Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 0-8218-4306-0 / 0821843060 |
ISBN-13 | 978-0-8218-4306-2 / 9780821843062 |
Zustand | Neuware |
Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Grundlagen – Anwendungen – Perspektiven
Buch | Softcover (2022)
Springer Vieweg (Verlag)
34,99 €
Eine Einführung in die Systemtheorie
Buch | Softcover (2022)
UTB (Verlag)
25,00 €