Algebraic Function Fields and Codes (Universitext) - Softcover

Stichtenoth, Henning

Softcover

ISBN 10: 0387564896 ISBN 13: 9780387564890

Publisher: Springer Verlag, 1993

Synopsis

This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.

About this title

Review

From the reviews of the second edition:

"In this book we have an exposition of the theory of function fields in one variable from the algebraic point of view ... . The book is carefully written, the concepts are well motivated and plenty of examples help to understand the ideas and proofs and so it can be used as a textbook for an introductory course on the (classical) arithmetic of function fields with an application to coding theory." (Felipe Zaldivar, MAA Online, January, 2009)

From the Back Cover

The theory of algebraic function fields has its origins in number theory, complex analysis (compact Riemann surfaces), and algebraic geometry. Since about 1980, function fields have found surprising applications in other branches of mathematics such as coding theory, cryptography, sphere packings and others. The main objective of this book is to provide a purely algebraic, self-contained and in-depth exposition of the theory of function fields.

This new edition, published in the series Graduate Texts in Mathematics, has been considerably expanded. Moreover, the present edition contains numerous exercises. Some of them are fairly easy and help the reader to understand the basic material. Other exercises are more advanced and cover additional material which could not be included in the text.

This volume is mainly addressed to graduate students in mathematics and theoretical computer science, cryptography, coding theory and electrical engineering.

Edition details

• Publisher: Springer Verlag
• Publication date: 1993
• Language: English
• ISBN 10: 0387564896
• ISBN 13: 9780387564890
• Binding: Paperback
• Number of pages: 260