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

Abstract : 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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https://hal-amu.archives-ouvertes.fr/hal-01478729
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Submitted on : Tuesday, February 28, 2017 - 12:19:12 PM
Last modification on : Tuesday, November 10, 2020 - 11:14:05 AM
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  • HAL Id : hal-01478729, version 1

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

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