Introduction to Coding Theory and Algebraic Geometry (Oberwolfach Seminars)

Jacobus H. van Lint and Gerard van Der Geer

ISBN 10: 3764322306 / ISBN 13: 9783764322304

Edité par Birkhäuser, 1988

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Type: Book N.B. Small plain label to inside front cover. Light crease to top corners of covers. N° de réf. du vendeur 054643

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Titre : Introduction to Coding Theory and Algebraic ...

Éditeur : Birkhäuser

Date d'édition : 1988

Reliure : Paperback

Etat : Very Good

Etat de la jaquette : No d/j as Published

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Synopsis :

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.