Algebraic function fields and codes / Henning Stichtenoth.
"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 include...
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| Main Author: | |
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| Format: | Ebook |
| Language: | English |
| Published: |
Berlin :
Springer,
[2009]
|
| Edition: | Second edition. |
| Series: | Graduate texts in mathematics ;
254. |
| Subjects: | |
| Online Access: | Springer eBooks |
| Summary: | "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."--Publisher's website. |
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| Item Description: | Previous edition: 1993. |
| Physical Description: | 1 online resource (xiii, 355 pages) : illustrations. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 3540768777 9783540768777 1282006436 9781282006430 3540768785 9783540768784 |