Algebraic Function Fields and Codes

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

Well-established popular textbook

Includes supplementary material: [...]

Inhaltsverzeichnis

Foundations of the Theory of Algebraic Function Fields.- Algebraic Geometry Codes.- Extensions of Algebraic Function Fields.- Differentials of Algebraic Function Fields.- Algebraic Function Fields over Finite Constant Fields.- Examples of Algebraic Function Fields.- Asymptotic Bounds for the Number of Rational Places.- More about Algebraic Geometry Codes.- Subfield Subcodes and Trace Codes.

Erscheinungsjahr:	2010
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Graduate Texts in Mathematics
Inhalt:	xiv 360 S.
ISBN-13:	9783642095566
ISBN-10:	3642095569
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Stichtenoth, Henning
Auflage:	Softcover reprint of hardcover 2nd edition 2008
Hersteller:	Springer Springer-Verlag GmbH Graduate Texts in Mathematics
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 21 mm
Von/Mit:	Henning Stichtenoth
Erscheinungsdatum:	18.11.2010
Gewicht:	0,569 kg