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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.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
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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Introduction to coding theory and algebraic geometry. Deutsche Mathematiker-Vereinigung: DMV-Seminar ; Bd. 12
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Basel ; Boston ; Berlin : Birkhäuser Verlag, 1988
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ISBN 13: 9783764322304
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Broschiert. Condizione: Gut. 83 Seiten Das Buch befindet sich in einem ordentlich erhaltenen Zustand. In ENGLISCHER Sprache. Sprache: Englisch Gewicht in Gramm: 160. Codice articolo 1705000
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Introduction to Coding Theory and Algebraic Geometry (DMV Seminar) (Volume 12)
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Condizione: Poor. Volume 12. This is an ex-library book and may have the usual library/used-book markings inside.This book has soft covers. In poor condition, suitable as a reading copy. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,250grams, ISBN:3764322306. Codice articolo 9786236
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Introduction to Coding Theory and Algebraic Geometry (Oberwolfach Seminars, 12)
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Condizione: Fine. First edition, first printing, 85 pp., paperback, fine. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country. Codice articolo ZB1358958
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Introduction to coding theory and algebraic geometry. DMV Seminar 12.
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Softcover. Condizione: Gut. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 14 LIN 9783764322304 Sprache: Englisch Gewicht in Gramm: 550. Codice articolo 2503338
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Introduction to Coding Theory and Algebraic Geometry (Oberwolfach Seminars)
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Introduction to Coding Theory and Algebraic Geometry
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Birkhäuser Basel, Springer Basel Sep 1988, 1988
ISBN 10: 3764322306
ISBN 13: 9783764322304
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Taschenbuch. Condizione: Neu. 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. 88 pp. Englisch. Codice articolo 9783764322304
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Introduction to Coding Theory and Algebraic Geometry
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Introduction to Coding Theory and Algebraic Geometry.
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ISBN 10: 3764322306
ISBN 13: 9783764322304
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Softcover. Condizione: Sehr gut. Basel, Birkhäuser 1988. gr.8°. 83 p. Pbck. DMV Seminar, 12.- Small ownership inscription verso cover and on title. Codice articolo 73747
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