Algebraic Function Fields and Codes

By:

Henning Stichtenoth

Format:

Paperback / softback

Series:

Graduate Texts in Mathematics,

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Description

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.

Release date Australia

November 18th, 2010

Author

Henning Stichtenoth

Audience

Professional & Vocational

Edition

Softcover reprint of hardcover 2nd ed. 2008

Illustrations

XIV, 360 p.

Pages

360

Series

Graduate Texts in Mathematics,

Dimensions

156x234x19

ISBN-13

9783642095566

Product ID

11084326

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