Decoding by rank-2 bundles over plane quartics
type: Item
instance of: scholarly article
title: Decoding by rank-2 bundles over plane quartics
zbMATH Open document ID: 1196.14033
author: Drue Coles
author: Emma Previato
published in: Journal of Symbolic Computation
publication date: 2010-06-11T00:00:00Z
review text: Let \(X\) be a smooth curve of genus \(g\) defined over a finite field. \textit{T. Johnsen} [Int. J. Pure Appl. Math. 4, No. 1, 33--45 (2003; Zbl 1054.14031)] established a connection between Goppa codes based on divisors of \(X\) and rank-\(2\) bundles over \(X\). In the paper under review some steps are sketched towards a decoding algorithm based on the explicit construction of the rank-\(2\) bundle atached to a syndrome, as a \(2\)-extension of linear bundles. To this purpose it is necessary to detect subbundles in terms of given transition matrices of the rank-\(2\) bundle. Some examples are worked out for codes arising from Klein's quartic over a finite field of characteristic two.
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 14G50
Mathematics Subject Classification ID: 94B27
zbMATH DE Number: 5720156
zbMATH Keywords: Goppa codes
zbMATH Keywords: vector bundles
zbMATH Keywords: Klein curve
reviewed by: Enric Nart
MaRDI profile type: Publication
full work available at URL: j.jsc.2010.03.009
OpenAlex ID: W2074447042
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DOI: 10.1016/J.JSC.2010.03.009
description: scientific article; zbMATH DE number 5720156