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Student Mathematical Library: Codes and Curves by American Mathem American Mathem (2000, Trade Paperback)
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About this product
Product Identifiers
PublisherAmerican Mathematical Society
ISBN-10082182628X
ISBN-139780821826287
eBay Product ID (ePID)4038697858
Product Key Features
Number of Pages66 Pages
Publication NameCodes and Curves
LanguageEnglish
SubjectInformation Theory, Geometry / Algebraic
Publication Year2000
TypeTextbook
AuthorAmerican Mathem American Mathem
Subject AreaMathematics, Computers
SeriesStudent Mathematical Library
FormatTrade Paperback
Dimensions
Item Height0.2 in
Item Weight3.9 Oz
Item Length8.5 in
Item Width5.5 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN00-038112
Dewey Edition21
Series Volume Number7
IllustratedYes
Dewey Decimal003/.54
Table Of ContentIntroduction to coding theory; Bounds on codes; Algebraic curves; Nonsingularity and the genus; Points, functions, and divisors on curves; Algebraic geometry codes; Good codes from algebraic geometry; Abstract algebra review; Finite fields; Projects; Bibliography.
SynopsisWhen 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., 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 monograph is based on a series of lectures the author gave as part of the IAS/PCMI 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., Introduces algebraic geometric coding theory. This book 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.
LC Classification NumberQA268.W345 2000
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