MARC details
| 000 -LEADER |
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| fixed length control field |
03260nam a22003377a 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
OSt |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20250801152129.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
250801b |||||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780821826287 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9789349750296 (pbk.) |
| Terms of availability |
$ 49.00 |
| 040 ## - CATALOGING SOURCE |
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| Language of cataloging |
ENG |
| Transcribing agency |
IISER-BPR |
| Modifying agency |
IISER-BPR |
| 041 ## - LANGUAGE CODE |
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| Language code of text/sound track or separate title |
ENG |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
516.352 |
| Item number |
WAL |
| Edition number |
23rd |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Walker, Judy L. |
| 9 (RLIN) |
5562 |
| 222 ## - KEY TITLE |
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| Key title |
Mathematics |
| 245 ## - TITLE STATEMENT |
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| Title |
Codes and curves |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
1st Indian ed. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Rhode Island : |
| Name of publisher, distributor, etc |
American Mathematical Society, |
| Date of publication, distribution, etc |
c2006. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
|---|
| Place of publication, distribution, etc |
Hyderabad : |
| Name of publisher, distributor, etc |
University Press (India) Pvt. Ltd., |
| Date of publication, distribution, etc |
2025. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
x, 68 p. : |
| Other physical details |
ill. ; |
| Dimensions |
22cm. |
| 440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE |
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| Title |
Student Mathematical Library |
| Name of part/section of a work |
IAS/PARK City Mathematical Subseries |
| Volume number/sequential designation |
Vol. 7 |
| 9 (RLIN) |
4093 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes illustrations, appendices, and bibliographic references. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
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.<br/><br/>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.<br/><br/>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.<br/><br/>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.<br/><br/>This book is published in cooperation with IAS/Park City Mathematics Institute.<br/><br/>Readership: Undergraduates in mathematics; mathematicians interested in coding theory or algebraic geometry and the connections between the two subjects. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Geometry |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Analytic geometries |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebraic geometry |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Theory of curves |
| 9 (RLIN) |
3217 |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Coding theory |
| 9 (RLIN) |
4234 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Books |
