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Codes and Curves

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Judy L. Walker 作者
Amer Mathematical Society
译者
2000-6 出版日期
66 页数
USD 18.00 价格
Paperback
Student Mathematical Library 丛书系列
9780821826287 图书编码

Codes and Curves 在线电子书 图书标签: 数学  编码  几何  代数  科普  代数曲线  代数几何7  代数几何   


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Codes and Curves 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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Codes and Curves 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024



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Codes and Curves 在线电子书 著者简介

Judy L. Walker: University of Nebraska, Lincoln, NE


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Codes and Curves 在线电子书 pdf 下载 txt下载 epub 下载 mobi 在线电子书下载

Codes and Curves 在线电子书 图书描述

When information is transmitted, errors are likely to occur. This problem has become increasingly important as tremendous amounts of information are transferred electronically every day. Coding theory examines efficient ways of packaging data so that these errors can be detected, or even corrected.

The traditional tools of coding theory have come from combinatorics and group theory. Since the work of Goppa in the late 1970s, however, coding theorists have added techniques from algebraic geometry to their toolboxes. In particular, by re-interpreting the Reed-Solomon codes as coming from evaluating functions associated to divisors on the projective line, one can see how to define new codes based on other divisors or on other algebraic curves. For instance, using modular curves over finite fields, Tsfasman, Vladut, and Zink showed that one can define a sequence of codes with asymptotically better parameters than any previously known codes.

This book is based on a series of lectures the author gave as part of the IAS/Park City Mathematics Institute (Utah) program on arithmetic algebraic geometry. Here, the reader is introduced to the exciting field of algebraic geometric coding theory. Presenting the material in the same conversational tone of the lectures, the author covers linear codes, including cyclic codes, and both bounds and asymptotic bounds on the parameters of codes. Algebraic geometry is introduced, with particular attention given to projective curves, rational functions and divisors. The construction of algebraic geometric codes is given, and the Tsfasman-Vladut-Zink result mentioned above is discussed.

No previous experience in coding theory or algebraic geometry is required. Some familiarity with abstract algebra, in particular finite fields, is assumed. However, this material is reviewed in two appendices. There is also an appendix containing projects that explore other codes not covered in the main text.

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