Error-Correcting Codes from Higher-Dimensional Varieties
✍ Scribed by Søren Have Hansen
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 424 KB
- Volume
- 7
- Category
- Article
- ISSN
- 1071-5797
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✦ Synopsis
In this paper we use intersection theory to develop methods for obtaining lower bounds on the parameters of algebraic geometric error-correcting codes constructed from varieties of arbitrary dimension. The methods are su$ciently general to encompass many of the codes previously constructed from higher-dimensional varieties, as well as those coming from curves. And still, the bounds obtained are usually as good as the ones previously known (at least of the same order of magnitude with respect to the size of the ground "eld). Several examples coming from De-ligne}Lusztig varieties, complete intersections of Hermitian hyper-surfaces, and from ruled surfaces (or more generally, projective bundles over a curve) are given. 2001 Academic Press