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Pré-Publication, Document De Travail Année : 2017

Hypersurfaces in weighted projective spaces over finite fields with applications to coding theory

Résumé

We consider the question of determining the maximum number of Fq-rational points that can lie on a hypersurface of a given degree in a weighted projective space over the finite field Fq, or in other words, the maximum number of zeros that a weighted homogeneous polynomial of a given degree can have in the corresponding weighted projective space over Fq. In the case of classical projective spaces, this question has been answered by J.-P. Serre. In the case of weighted projective spaces, we give some conjectures and partial results. Applications to coding theory are included and an appendix providing a brief compendium of results about weighted projective spaces is also included.
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Dates et versions

hal-01478729 , version 1 (28-02-2017)
hal-01478729 , version 2 (22-06-2017)

Identifiants

  • HAL Id : hal-01478729 , version 1

Citer

Yves Aubry, Wouter Castryck, Sudhir R Ghorpade, Gilles Lachaud, Michael E O 'Sullivan, et al.. Hypersurfaces in weighted projective spaces over finite fields with applications to coding theory. 2017. ⟨hal-01478729v1⟩
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