Name
Title | ||
|---|---|---|
Hypersurfaces in weighted projective spaces over finite fields with applications to coding theory. |
Abstract | ||
|---|---|---|
We consider the question of determining the maximum number of (mathbb{F}_{q})-rational points that can lie on a hypersurface of a given degree in a weighted projective space over the finite field (mathbb{F}_{q}), 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 (mathbb{F}_{q}). 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. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/978-3-319-63931-4_2 | arXiv: Algebraic Geometry |
Field | DocType | Volume |
Topology,Combinatorics,Twisted cubic,Complex projective space,Homogeneous polynomial,Weighted projective space,Quaternionic projective space,Projective linear group,Collineation,Mathematics,Projective space | Journal | abs/1706.03050 |
ISSN | Citations | PageRank |
E.W. Howe et al. (eds.), Algebraic Geometry for Coding Theory and
Cryptography, Association for Women in Mathematics Series Vol. 9, Springer,
New York, 2017, 37 pp | 0 | 0.34 |
References | Authors | |
2 | 6 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yves Aubry | 1 | 0 | 0.34 |
| Wouter Castryck | 2 | 58 | 9.43 |
| Sudhir R. Ghorpade | 3 | 80 | 12.16 |
| Gilles Lachaud | 4 | 41 | 8.53 |
| Michael E. O'Sullivan | 5 | 0 | 0.68 |
| Samrith Ram | 6 | 20 | 3.52 |