Title :

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

Author(s) :

Aubry, Yves [Auteur]
Institut de Mathématiques de Marseille [I2M]
Institut de Mathématiques de Toulon - EA 2134 [IMATH]
Castryck, Wouter [Auteur]
Catholic University of Leuven = Katholieke Universiteit Leuven [KU Leuven]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Ghorpade, Sudhir [Auteur]
Indian Institute of Technology Bombay [IIT Bombay]
Lachaud, Gilles [Auteur]
Institut de Mathématiques de Marseille [I2M]
O 'Sullivan, Michael [Auteur]
San Diego State University [SDSU]
Ram, Samrith [Auteur]

Scientific editor(s) :

Howe E.
Lauter K.
Walker J.

Conference title :

Algebraic Geometry for Coding Theory and Cryptography

Conference organizers(s) :

IPAM (UCLA)

City :

Los Angeles

Country :

Etats-Unis d'Amérique

Start date of the conference :

2016-02-22

Book title :

Algebraic Geometry for Coding Theory and Cryptography

Publisher :

Springer, Cham

Publication date :

2017-11-16

HAL domain(s) :

Mathématiques [math]/Géométrie algébrique [math.AG]
Informatique [cs]/Théorie de l'information [cs.IT]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

European Project :

Post-quantum cryptography for long-term security
Motivic Mellin transforms and exponential sums through non-archimedean geometry

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL