We study the algebraic geometry of a family of evaluation codes from planesmooth curves defined over any field. In particular, we provide a cohomologicalcharacterization of their dual minimum distance. After having discussed somegeneral results on zero-dimensional subschemes of the plane, we focus on theinteresting case of Hermitians-point codes, describing the geometry of their dualminimum-weight codewords.© 2014 Elsevier B.V. All rights reserved.
A zero-dimensional approach to Hermitian codes / Ballico, Edoardo; Ravagnani, Alberto. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - STAMPA. - 219:4(2015), pp. 1031-1044. [10.1016/j.jpaa.2014.05.031]
A zero-dimensional approach to Hermitian codes
Ballico, Edoardo;
2015-01-01
Abstract
We study the algebraic geometry of a family of evaluation codes from planesmooth curves defined over any field. In particular, we provide a cohomologicalcharacterization of their dual minimum distance. After having discussed somegeneral results on zero-dimensional subschemes of the plane, we focus on theinteresting case of Hermitians-point codes, describing the geometry of their dualminimum-weight codewords.© 2014 Elsevier B.V. All rights reserved.| File | Dimensione | Formato | |
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