Overview

This book has two objectives. The first is to fill a void inthe existing mathematical literature by providing a modern,self-contained and in-depth exposition of the theory ofalgebraic function fields. Topics include the Riemann-Rochtheorem, algebraic extensions of function fields,ramifications theory and differentials. Particular emphasisis placed on function fields over a finite constant field,leading into zeta functins and the Hasse-Weil theorem.Numerous examples illustrate the general theory.Error-correcting codes are in widespread use for thereliable transmission of information. Perhaps the mostfascinating of all the ties that link the theory of thesecodes to mathematics is the construction by V.D. Goppa, ofpowerful codes using techniques borrowed fromalgebraicgeometry. Algebraic function fields provide the mostelementary approach to Goppa's ideas, and the secondobjective of this book is to provide an introduction toGoppa's algebraic-geometric codesalong these lines. Thecodes, their parameters and links with traditional codessuch as classical Goppa, Peed-Solomon and BCH codes aretreated atan early stage of the book. Subsequent chaptersinclude a decoding algorithmfor these codes as well as adiscussion of their subfield subcodes and tracecodes.Stichtenoth's book will be very useful to students andresearchers in algebraic geometry and coding theory and tocomputer scientists and engineers interested in informationtransmission.

Full Product Details

Author:   Henning Stichtenoth
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Dimensions:   Width: 13.80cm , Height: 1.80cm , Length: 21.60cm
Weight:   0.421kg
ISBN:  

9783540564898

ISBN 10:   3540564896
Pages:   270
Publication Date:   25 June 1993
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

1. Foundations of the Theory of Algebraic Function Fiels.- 2. Geometric Goppa Codes.- 3. Extensions of Algebraic Function Fields.- 4. Differentials of Algebraic Function Fields.- 5. Algebraic Function Fields over Finite Constant Fields.- 6. Examples of Algebraic Function Fields.- 7. More about Geometric Goppy Codes.- 8. Subfield Subcodes and Trace Codes.- Appendix A. Field Theory.- Appendix B. Algebraic Curves and Algebraic Function Fields.- Bibliography.- List of Notations.- Index

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