Title | Algorithms for checking uniformity conditions and applications in coding theory |
Author(s) | Martin Kreuzer |
Type | Article in Conference Proceedings |
Abstract | In 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. |
Keywords | |
Length | 9 |
File |
|
Language | English |
Series | Queen's Papers in Pure and Applied Mathematics |
Volume | 123 |
Pages | C1-C9 |
Publisher | Queen's University |
Address | Kingston/Canada |
Year | 2002 |
Editor | A. V. Geramita |
Edition | 0 |
Translation |
No |
Refereed |
Yes |
Book | Zero-Dimensional Schemes and Applications |
Conferencename | Workshop "Zero-Dimensional Schemes and Applications" 2000 (Naples/Italy) |