Introduction to Coding Theory and Algebraic Geometry
Jacobus H.van Lint
ISBN 10: 3034899793 ISBN 13: 9783034899796
Editore: Birkhäuser Basel, 2013
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1988 edition. 86 pages. 9.85x6.69x0.20 inches. In Stock. Codice articolo 3034899793
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These notes are based on lectures given in the semmar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Diisseldorf, November 16-21, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the Gilbert-Varshamov bound. The result was considered sensational. Furthermore, it was surprising to see these unrelated areas of mathematics collaborating. The aim of this course is to give an introduction to coding theory and to sketch the ideas of algebraic geometry that led to the new result. Finally, a number of applications of these methods of algebraic geometry to coding theory are given. Since this is a new area, there are presently no references where one can find a more extensive treatment of all the material. However, both for algebraic geometry and for coding theory excellent textbooks are available. The combination ofthe two subjects can only be found in a number ofsurvey papers. A book by C. Moreno with a complete treatment of this area is in preparation. We hope that these notes will stimulate further research and collaboration of algebraic geometers and coding theorists. G. van der Geer, J.H. van Lint Introduction to CodingTheory and Algebraic Geometry PartI -- CodingTheory Jacobus H. vanLint 11 1. Finite fields In this chapter we collect (without proof) the facts from the theory of finite fields that we shall need in this course.
Contenuti: I: Coding Theory.- 1. Finite fields.- 2. Error-correcting codes.- 3. Linear codes.- 4. Cyclic codes.- 5. Classical Goppa codes.- 6. Bounds on codes.- 7. Self-dual codes.- 8. Codes from curves.- References.- II: Algebraic Geometry.- I. Elementary concepts from algebraic geometry.- II. Divisors on algebraic curves.- III. Goppa Codes.- IV. Couting points on curves over finite fields.- V. Shimura curves and codes.- Index of notations.
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Titolo: Introduction to Coding Theory and Algebraic ...
Casa editrice: Birkhäuser Basel
Data di pubblicazione: 2013
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Introduction to Coding Theory and Algebraic Geometry (eng)
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. I: Coding Theory.- 1. Finite fields.- 2. Error-correcting codes.- 3. Linear codes.- 4. Cyclic codes.- 5. Classical Goppa codes.- 6. Bounds on codes.- 7. Self-dual codes.- 8. Codes from curves.- References.- II: Algebraic Geometry.- I. Elementary concepts fr. Codice articolo 4319776
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - These notes are based on lectures given in the semmar on 'Coding Theory and Algebraic Geometry' held at Schloss Mickeln, Diisseldorf, November 16-21, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the Gilbert-Varshamov bound. The result was considered sensational. Furthermore, it was surprising to see these unrelated areas of mathematics collaborating. The aim of this course is to give an introduction to coding theory and to sketch the ideas of algebraic geometry that led to the new result. Finally, a number of applications of these methods of algebraic geometry to coding theory are given. Since this is a new area, there are presently no references where one can find a more extensive treatment of all the material. However, both for algebraic geometry and for coding theory excellent textbooks are available. The combination ofthe two subjects can only be found in a number ofsurvey papers. A book by C. Moreno with a complete treatment of this area is in preparation. We hope that these notes will stimulate further research and collaboration of algebraic geometers and coding theorists. G. van der Geer, J.H. van Lint Introduction to CodingTheory and Algebraic Geometry PartI -- CodingTheory Jacobus H. vanLint 11 1. Finite fields In this chapter we collect (without proof) the facts from the theory of finite fields that we shall need in this course. Codice articolo 9783034899796
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Introduction to Coding Theory and Algebraic Geometry
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Springer, Basel, Birkhäuser Basel Okt 2011, 2011
ISBN 10: 3034899793
ISBN 13: 9783034899796
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -These notes are based on lectures given in the semmar on 'Coding Theory and Algebraic Geometry' held at Schloss Mickeln, Diisseldorf, November 16-21, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the Gilbert-Varshamov bound. The result was considered sensational. Furthermore, it was surprising to see these unrelated areas of mathematics collaborating. The aim of this course is to give an introduction to coding theory and to sketch the ideas of algebraic geometry that led to the new result. Finally, a number of applications of these methods of algebraic geometry to coding theory are given. Since this is a new area, there are presently no references where one can find a more extensive treatment of all the material. However, both for algebraic geometry and for coding theory excellent textbooks are available. The combination ofthe two subjects can only be found in a number ofsurvey papers. A book by C. Moreno with a complete treatment of this area is in preparation. We hope that these notes will stimulate further research and collaboration of algebraic geometers and coding theorists. G. van der Geer, J.H. van Lint Introduction to CodingTheory and Algebraic Geometry PartI -- CodingTheory Jacobus H. vanLint 11 1. Finite fields In this chapter we collect (without proof) the facts from the theory of finite fields that we shall need in this course. 85 pp. Englisch. Codice articolo 9783034899796
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Introduction to Coding Theory and Algebraic Geometry
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Birkhäuser, Birkhäuser Okt 2011, 2011
ISBN 10: 3034899793
ISBN 13: 9783034899796
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -I: Coding Theory.- 1. Finite fields.- 2. Error-correcting codes.- 3. Linear codes.- 4. Cyclic codes.- 5. Classical Goppa codes.- 6. Bounds on codes.- 7. Self-dual codes.- 8. Codes from curves.- References.- II: Algebraic Geometry.- I. Elementary concepts from algebraic geometry.- II. Divisors on algebraic curves.- III. Goppa Codes.- IV. Couting points on curves over finite fields.- V. Shimura curves and codes.- Index of notations.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 88 pp. Englisch. Codice articolo 9783034899796
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Taschenbuch. Condizione: Neu. Introduction to Coding Theory and Algebraic Geometry | J. van Lint (u. a.) | Taschenbuch | 85 S. | Englisch | 2011 | Birkhäuser | EAN 9783034899796 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Codice articolo 105390894
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Paperback. Condizione: Brand New. 1988 edition. 86 pages. 9.85x6.69x0.20 inches. In Stock. Codice articolo __3034899793
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