Algebraic Function Fields and Codes by Henning Stichtenoth

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Algebraic Function Fields and Codes by Henning Stichtenoth

Regular price $64.99
Condition - New
40+ In stock
Regular price $64.99
Condition - New
40+ In stock

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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. The codes which are constructed from algebraic function ?elds were ?rst introduced by V.

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Algebraic Function Fields and Codes by 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 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.

From the reviews of the second edition:

"In this book we have an exposition of the theory of function fields in one variable from the algebraic point of view …The book is carefully written, the concepts are well motivated and plenty of examples help to understand the ideas and proofs and so it can be used as a textbook for an introductory course on the (classical) arithmetic of function fields with an application to coding theory." (Felipe Zaldivar, MAA Online, January, 2009)

SKU NIN9783642095566
ISBN 13 9783642095566
ISBN 10 3642095569
Title Algebraic Function Fields and Codes
Author Henning Stichtenoth
Series Graduate Texts In Mathematics
Condition New
Binding Type Paperback
Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Year published 2010-11-18
Number of pages 360
Cover note Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note This is a new book - be the first to read this copy. With untouched pages and a perfect binding, your brand new copy is ready to be opened for the first time