Decoding of algebraic-geometric codes

Michael A. Tsfasman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A decade ago the problem of decoding algebraic-geometric codes looked hardly tangible and rather far from algebraic geometry. Both proved to be wrong. The break-through, started by Justesen during his visit to Moscow in 1988, last year reached the point of decoding algebraic-geometric codes up to half the designed minimum distance. This illustrious achievement is due to the work of many mathematicians, including Vladut, Skorobogatov, Larsen, Havemose, Elbrond Jensen, Hoholdt, Porter, Krachkovskii, Pellikaan, and Shen, the final result being obtained by Ehrhard, Feng, Rao, and Duursma. The algorithms we have now are both of reasonable complexity and rather easy to understand. However they do tangle several specifical difficulties of algebraic geometry nature. In this talk the principal points of these decoding algorithms will be described for the simplest example of the curve being the line, with the difficulties of the general case being pointed out on the way.

Original languageEnglish
Title of host publicationProceedings of the 1993 IEEE International Symposium on Information Theory
PublisherPubl by IEEE
Number of pages1
ISBN (Print)0780308786
Publication statusPublished - 1993
Externally publishedYes
EventProceedings of the 1993 IEEE International Symposium on Information Theory - San Antonio, TX, USA
Duration: 17 Jan 199322 Jan 1993

Publication series

NameProceedings of the 1993 IEEE International Symposium on Information Theory

Conference

ConferenceProceedings of the 1993 IEEE International Symposium on Information Theory
CitySan Antonio, TX, USA
Period17/01/9322/01/93

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