Highest numbers of points of hypersurfaces over finite fields and generalized Reed--Muller codes

  • Authors:

  • FrançOis Rodier;Adnen Sboui

  • Affiliations:

  • Institut de Mathématiques de Luminy, CNRS, 163 avenue de Luminy, Case 907, Marseille Cedex 9, France;Institut de Mathématiques de Luminy, CNRS, 163 avenue de Luminy, Case 907, Marseille Cedex 9, France

  • Venue:
  • Finite Fields and Their Applications
  • Year:
  • 2008

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Abstract

The weight distribution of the generalized Reed-Muller codes over the finite field F"q is linked to the number of points of some hypersurfaces of degree d in the n-dimensional space over the same field. For d=