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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.
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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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- EditoreBirkhäuser Basel
- Data di pubblicazione1989
- ISBN 10 3764322306
- ISBN 13 9783764322304
- RilegaturaCopertina flessibile
- LinguaInglese
- Numero di pagine88
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Introduction to coding theory and algebraic geometry. Deutsche Mathematiker-Vereinigung: DMV-Seminar ; Bd. 12
Editore:
Basel ; Boston ; Berlin : Birkhäuser Verlag, 1988
ISBN 10: 3764322306
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.
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Basel, Birkhauser, 1988
ISBN 10: 3764322306
ISBN 13: 9783764322304
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Introduction to Coding Theory and Algebraic Geometry (Oberwolfach Seminars)
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Softcover. Condizione: Bon. Ancien livre de bibliothèque. Traces d'usure sur la couverture. Petite(s) trace(s) de pliure sur la couverture. Salissures sur la tranche. Edition 1988. Ammareal reverse jusqu'à 15% du prix net de cet article à des organisations caritatives. ENGLISH DESCRIPTION Book Condition: Used, Good. Former library book. Signs of wear on the cover. Slightly creased cover. Stains on the edge. Edition 1988. Ammareal gives back up to 15% of this item's net price to charity organizations. Codice articolo E-927-354
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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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Introduction to Coding Theory and Algebraic Geometry
Editore:
Birkhäuser Basel, Springer Basel Sep 1988, 1988
ISBN 10: 3764322306
ISBN 13: 9783764322304
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Taschenbuch
Da: Rheinberg-Buch Andreas Meier eK, Bergisch Gladbach, Germania
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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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Immagini fornite dal venditore
Introduction to Coding Theory and Algebraic Geometry
Editore:
Birkhäuser Basel, Springer Basel Sep 1988, 1988
ISBN 10: 3764322306
ISBN 13: 9783764322304
Nuovo
Taschenbuch
Da: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germania
Valutazione del venditore 5 su 5 stelle
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
Quantità: 1 disponibili