A zero-dimensional approach to Hermitian codes

• Edoardo Ballico ^[1] ; Alberto Ravagnani ^[2]
  1. [1] University of Trento

     University of Trento

     Trento, Italia

     
  2. [2] University of Neuchâtel

     University of Neuchâtel

     Neuchâtel, Suiza

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 4 ((April 2015) ), 2015, págs. 1031-1044
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.05.031
• Enlaces
  • Texto completo
• Resumen

  • We study the algebraic geometry of a family of evaluation codes from plane smooth curves defined over any field. In particular, we provide a cohomological characterization of their dual minimum distance. After having discussed some general results on zero-dimensional subschemes of the plane, we focus on the interesting case of Hermitian s-point codes, describing the geometry of their dual minimum-weight codewords.