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Titlebook: Algebraic Function Fields and Codes; Henning Stichtenoth Textbook 2009Latest edition Springer-Verlag Berlin Heidelberg 2009 Algebra.Algebr

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期刊全称Algebraic Function Fields and Codes
影响因子2023Henning Stichtenoth
视频video
发行地址Well-established popular textbook.Includes supplementary material:
学科分类Graduate Texts in Mathematics
图书封面Titlebook: Algebraic Function Fields and Codes;  Henning Stichtenoth Textbook 2009Latest edition Springer-Verlag Berlin Heidelberg 2009 Algebra.Algebr
影响因子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 gen
Pindex Textbook 2009Latest edition
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Textbook 2009Latest editionthe 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, oth
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0072-5285 he 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
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Examples of Algebraic Function Fields,erve as an illustration of the general theory of algebraic function fields developed in Chapters 1, 3, 4 and 5. Some of the examples will be used in Chapter 8 for the construction of algebraic geometry codes..This assumption is not essential; actually most results of Chapter 6 hold for an arbitrary constant field ., with minor modifications.
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Anton Stipeč,Biljana Mileva Boshkoska-Weil Bound (see Theorem 5.2.3). This bound has many number-theoretical implications, and it plays a crucial role in the applications of algebraic function fields to coding theory, cf. Chapter 8 and 9.
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