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. Readership Graduate students and research mathematicians interested in algebraic geometry and coding theory. Reviews "...the authors have done a great service to the mathematical community. Written in an utmost lucid and thorough style, this book on a rapidly growing new area of contemporary, interdisciplinary mathematics, together with its forthcoming companion volume "Advanced Chapters", must be seen as the most profound and topical exposition of its kind. It is of nearly universal utility for both specialists and non-specialists in the field, and it is very likely to become the unrivalled standard text in the related literature. We share the authors' hope that this monograph will have a propelling impact, and that it will be of some use for those who intend to choose algebraic geometric coding theory as their own area of research in the future." *-- Zentralblatt MATH* "The book under review successfully introduces the necessary background needed for the study of AG codes. ...it will be a standard reference for beginners as well as for active researchers in this beautiful subject." *-- Mathematical Reviews* |