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Evaluation codes at singular points of algebraic differential equations |
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| Authors: | A Campillo J I Farran M J Pisabarro |
| Affiliation: | (1) Departamento de Algebra, Geometria y Topologia, Universidad de Valladolid, Valladolid, Spain;(2) Departamento de Matematica Aplicada, University of Valladolid, Valladolid, Spain;(3) Departamento de Matematicas, Universidad de León, León, Spain |
| Abstract: | We use the special geometry of singular points of algebraic differential equations on the affine plane over finite fields to study the main features and parameters of error correcting codes giving by evaluating functions at sets of singular points. In particular, one gets new methods to construct codes with designed minimum distance. This work was partially supported by MCyT BFM2001-2251. |
| Keywords: | Evaluation codes Algebraic differential equations Cayley– Bacharach theorem Designed minimum distance |
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