Conference papers
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.
https://hal-amu.archives-ouvertes.fr/hal-01478729
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Submitted on : Thursday, June 22, 2017 - 11:45:55 AM
Last modification on : Sunday, November 29, 2020 - 3:24:00 AM
Long-term archiving on: : Wednesday, January 10, 2018 - 2:13:08 PM
Contributor : Aigle I2m Connect in order to contact the contributor
Submitted on : Thursday, June 22, 2017 - 11:45:55 AM
Last modification on : Sunday, November 29, 2020 - 3:24:00 AM
Long-term archiving on: : Wednesday, January 10, 2018 - 2:13:08 PM
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