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#### Algebraic Function Fields and Codes

 Tác giả: Henning Stichtenoth Loại tài liệu: Sách điện tử
 Nội dung tóm tắt: 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

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#### Thông tin chi tiết

 Dạng tài liệu: Bản điện tử Tác giả: Henning Stichtenoth Nhà xuất bản: Springer Năm xuất bản: 2009 Mô tả vật lý: Từ khóa: Algebra, Algebraische Funktionenkörper, Codierungstheorie, Funktionen, algebraic curves, algebraic function fields, algebraic geometric codes