Algebraic Function Fields and Codes

Henning Stichtenoth

ISBN 10: 3540768777 / ISBN 13: 9783540768777

Editore: Springer, Berlin, Springer Berlin Heidelberg, Springer, 2008

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Druck auf Anfrage Neuware - Printed after ordering - 15 years after the rst printing of Algebraic Function Fields and Codes,the mathematics editors of Springer Verlag encouraged me to revise and extend the book. Besides numerous minor corrections and amendments, the second edition di ers from the rst one in two respects. Firstly I have included a series of exercises at the end of each chapter. Some of these exercises are fairly easy and should help the reader to understand the basic concepts, others are more advanced and cover additional material. Secondly a new chapter titled 'Asymptotic Bounds for the Number of Rational Places' has been added. This chapter contains a detailed presentation of the asymptotic theory of function elds over nite elds, including the explicit construction of some asymptotically good and optimal towers. Based on these towers, a complete and self-contained proof of the Tsfasman-Vladut-Zink Theorem is given. This theorem is perhaps the most beautiful application of function elds to coding theory. The codes which are constructed from algebraic function elds were rst introduced by V. D. Goppa. Accordingly I referred to them in the rst edition as geometric Goppa codes. Since this terminology has not generally been - cepted in the literature, I now use the more common term algebraic geometry codes or AG codes. I would like to thank Alp Bassa, Arnaldo Garcia, Cem Guneri, Sevan Harput and Alev Topuzo glu for their help in preparing the second edition.

Codice articolo 9783540768777

Dati bibliografici

• Titolo: Algebraic Function Fields and Codes
• Editore: Springer, Berlin, Springer Berlin Heidelberg, Springer
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 3540768777
• ISBN 13: 9783540768777
• Rilegatura: Buch
• Edizione: seconda edizione
• Condizione: Neu
• Dimensioni: 240 L x 159 A x 26 P (millimetri) 240 millimetri di larghezza per 159 millimetri di altezza per 26 millimetri di profondità
• Peso: 736 grammi

Descrizione articolo

Riassunto

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.

Dalla quarta di copertina

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.