Name
Title | ||
|---|---|---|
On a conjecture of Tsfasman and an inequality of Serre for the number of points on hypersurfaces over finite fields. |
Abstract | ||
|---|---|---|
We give a short proof of an inequality, conjectured by Tsfasman and proved by Serre, for the maximum number of points on hypersurfaces over finite fields. Further, we consider a conjectural extension, due to Tsfasman and Boguslavsky, of this inequality to an explicit formula for the maximum number of common solutions of a system of linearly independent multivariate homogeneous polynomials of the same degree with coefficients in a finite field. This conjecture is shown to be false, in general, but is also shown to hold in the affirmative in a special case. Applications to generalized Hamming weights of projective Reed-Muller codes are outlined and a comparison with an older conjecture of Lachaud and a recent result of Couvreur is given. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.17323/1609-4514-2015-15-4-715-725 | MOSCOW MATHEMATICAL JOURNAL |
Keywords | DocType | Volume |
Hypersurface,rational point,finite field,Veronese variety,Reed-Muller code,generalized Hamming weight | Journal | 15 |
Issue | ISSN | Citations |
4 | 1609-3321 | 1 |
PageRank | References | Authors |
0.48 | 4 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mrinmoy Datta | 1 | 1 | 0.48 |
| Sudhir R. Ghorpade | 2 | 80 | 12.16 |