Algebraic Function Fields and Codes

Stichtenoth, Henning

ISBN 10: 3540564896 / ISBN 13: 9783540564898

Published by Springer, 1993

About this Item

Trade paperback. Square Tight Binding.Mild rubbing to wraps. Clean interior, save for p/o signature to front end paper and very sporadic pencil marginalia. A nice edition at an attractive price.

Seller Inventory # 10740

Bibliographic Details

• Title: Algebraic Function Fields and Codes
• Publisher: Springer
• Publication Date: 1993
• Language: English
• ISBN 10: 3540564896
• ISBN 13: 9783540564898
• Binding: Paperback
• Condition: Very Good

About this title

Synopsis

This book has two objectives. The first is to fill a void in the existing mathematical literature by providing a modern, self-contained and in-depth exposition of the theory of algebraic function fields. The topics include the Riemann-Roch theorem, algebraic extensions of function fields, ramifications theory and differentials. Particular emphasis is placed on function fields over a finite constant field, leading into zeta functions and the Hasse-Weil theorem. Numerous examples illustrate the general theory. Error-correcting codes are in widespread use for the reliable transmission of information. Perhaps the most fascinating of all the ties that link the theory of these codes to mathematics is the construction by V.D. Goppa, of powerful codes using techniques borrowed from algebraic geometry. Algebraic function fields provide the most elementary approach to Goppa's ideas, and the second objective of this book is to provide an introduction to Goppa's algebraic-geometric codes along these lines. The codes, their parameters and links with traditional codes such as classical Goppa, Peed-Solomon and BCH codes are treated at an early stage of the book. Subsequent chapters include a decoding algorithm for these codes as well as a discussion of their subfield subcodes and trace codes. Stichtenoth's book will be very useful to students and researchers in algebraic geometry and coding theory and to computer scientists and engineers interested in information transmission.

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)