# Codes and Curves (Student Mathematical Library, Vol. 7)

## Judy L. Walker

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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.

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From the Publisher:

A useful supplement to an undergraduate text in coding theory to give students a basic introduction to algebraic geometry codes. --Mathematical Reviews

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## 1.Codes and Curves (Student Mathematical Library, Vol. 7)

Editore: Amer Mathematical Society (2000)
ISBN 10: 082182628X ISBN 13: 9780821826287
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Descrizione libro Amer Mathematical Society, 2000. Paperback. Condizione libro: New. ABSOLUTELY BRAND NEW IN SHRINKWRAP!! SHIPS WITHIN 24 HOURS! Tracking Provided. DHL processing & USPS delivery for an average of 3-5 Day Standard & 2-3 Day Expedited! FREE INSURANCE! Fast & Personal Support! Careful Packaging. No Hassle, Full Refund Return Policy!. Codice libro della libreria mon0000566870

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## 2.Codes and Curves (Paperback)

Editore: American Mathematical Society, United States (2000)
ISBN 10: 082182628X ISBN 13: 9780821826287
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Descrizione libro American Mathematical Society, United States, 2000. Paperback. Condizione libro: New. Language: English . Brand New Book. 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. Codice libro della libreria AAN9780821826287

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## 3.Codes and Curves (Paperback)

Editore: American Mathematical Society, United States (2000)
ISBN 10: 082182628X ISBN 13: 9780821826287
Nuovi Paperback Quantità: 1
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Descrizione libro American Mathematical Society, United States, 2000. Paperback. Condizione libro: New. Language: English . Brand New Book. 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. Codice libro della libreria AAN9780821826287

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## 4.Codes and Curves (Student Mathematical Library, Vol. 7)

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ISBN 10: 082182628X ISBN 13: 9780821826287
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Descrizione libro Amer Mathematical Society, 2000. Paperback. Condizione libro: New. book. Codice libro della libreria 082182628X

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## 5.Codes and Curves

Editore: American Mathematical Society
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Descrizione libro American Mathematical Society. Paperback. Condizione libro: new. BRAND NEW, Codes and Curves, Judy L. Walker, 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. Codice libro della libreria B9780821826287

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## 6.Codes and Curves (Student Mathematical Library, Vol. 7) (Student Mathematical Library, V. 7.)

Editore: Amer Mathematical Society (2000)
ISBN 10: 082182628X ISBN 13: 9780821826287
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Descrizione libro Amer Mathematical Society, 2000. Paperback. Condizione libro: New. Brand new. We distribute directly for the publisher. 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. Codice libro della libreria 1006230003

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## 7.Codes And Curves

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## 8.Codes and Curves (Student Mathematical Library, Vol. 7)

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Descrizione libro Amer Mathematical Society, 2000. Paperback. Condizione libro: New. Codice libro della libreria DADAX082182628X

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## 9.Codes and Curves (Student Mathematical Library, Vol. 7) (Student Mathematical Library, V. 7.)

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Descrizione libro Amer Mathematical Society, 2000. Paperback. Condizione libro: Brand New. 66 pages. 8.00x5.50x0.25 inches. In Stock. Codice libro della libreria __082182628X

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## 10.Codes and Curves 7 by Judy L Walker 2000 Paperback

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Descrizione libro Condizione libro: Brand New. Book Condition: Brand New. Codice libro della libreria 97808218262871.0

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