Codes and Curves (Student Mathemati..., Walker, Judy L.

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Book Title
Codes and Curves (Student Mathematical Library)
ISBN
082182628X
EAN
9780821826287
Release Title
Codes and Curves (Student Mathematical Library)
Artist
Walker, Judy L.
Brand
N/A
Colour
N/A
Kategorie

Über dieses Produkt

Product Identifiers

Publisher
American Mathematical Society
ISBN-10
082182628X
ISBN-13
9780821826287
eBay Product ID (ePID)
4038697858

Product Key Features

Number of Pages
66 Pages
Language
English
Publication Name
Codes and Curves
Publication Year
2000
Subject
Information Theory, Geometry / Algebraic
Type
Textbook
Subject Area
Mathematics, Computers
Author
American Mathem American Mathem
Series
Student Mathematical Library
Format
Trade Paperback

Dimensions

Item Height
0.2 in
Item Weight
3.9 Oz
Item Length
8.5 in
Item Width
5.5 in

Additional Product Features

Intended Audience
Scholarly & Professional
LCCN
00-038112
Dewey Edition
21
Series Volume Number
7
Illustrated
Yes
Dewey Decimal
003/.54
Table Of Content
Introduction 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.
Synopsis
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., 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 Number
QA268.W345 2000

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