Algebraic function fields and codes
Algebraic function fields and codes
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DOI：
10.1007/978-3-540-76878-4
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发表时间：
1993-06
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影响因子：
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通讯作者：
H. Stichtenoth
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文献类型：
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作者：
H. Stichtenoth
15年后，？当我第一次印刷《代数函数域与代码》时，施普林格出版社的数学编辑鼓励我修改和扩充这本书。除了许多小的更正和修改，第二版迪？来自？第一个在两个方面。首先，我在每一章的末尾都做了一系列的练习。其中一些练习相当简单，应该有助于读者理解基本概念，其他练习则更高级，涵盖了额外的材料。第二，增加了一个新的章节，标题为“有理位置个数的渐近界”。本章包含了详细介绍的渐近理论的功能？结束了？nite？elds，包括一些渐近良好和最佳塔的明确建设。在此基础上，给出了Tsfasman-Vladut-Zink定理的一个完备的证明.这个定理也许是函数的最美丽的应用？编码理论的基础。由代数函数构造的编码？ELD是什么？由VD Goppa推出。因此，我提到他们在？几何Goppa码。由于这个术语在文献中还没有被普遍接受，我现在使用更常见的术语代数几何码或AG码。我要感谢Alp Bassa，Arnaldo Garcia，Cem Guneri，Mr. Sevan Harput和Alev Topuzo？感谢他们帮助准备第二版。
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 VD 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.