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TitleAlgorithms for checking uniformity conditions and applications in coding theory
Author(s) Martin Kreuzer
TypeArticle in Conference Proceedings
AbstractIn the first part of this paper we generalize the characterization
of Cayley-Bacharach schemes using liaison given by Geramita-K-Robbiano
to the non-reduced case. Then we show how one can apply this result to
develop an algorithm for checking the Cayley-Bacharach property
in the non-reduced case. We also discuss algorithms for checking higher
uniformity properties of reduced 0-dimensional schemes, in particular for
checking the $(i,j)$-uniformities introduced by the author. Using
Hansen's construction, we can interpret these algorithms as algorithms
for computing the minimal distance of a linear code. Possible generalizations
include a version of Hansen's construction for the nonreduced case and algorithms for checking $(i,j)$-uniformity in the non-reduced case.
KeywordsCayley-Bacharach property, Gröbner basis, colon ideal computation, linear code, minimal distance
Length9
File
LanguageEnglish
SeriesQueen's Papers in Pure and Applied Mathematics
Volume123
PagesC1-C9
PublisherQueen's University
AddressKingston/Canada
Year2002
EditorA. V. Geramita
Edition0
Translation No
Refereed Yes
BookZero-Dimensional Schemes and Applications
ConferencenameWorkshop "Zero-Dimensional Schemes and Applications" 2000 (Naples/Italy)
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