[Minimal and maximal arrangements of hyperplanes in ]
Dans cette Note on étudie les arrangements d'hyperplans dans un espace projectif tels que le nombre de points rationnels de la réunion de ces hyperplans soit minimal. Ces résultats ont des applications en théorie des codes.
In this Note we study the arrangements of hyperplanes in a projective space such that the number of rational points of the union of these hyperplanes is minimal. These results apply to coding theory.
Accepted:
Published online:
Rodier, François 1; Sboui, Adnen 1
@article{CRMATH_2007__344_5_287_0,
author = {Rodier, Fran\c{c}ois and Sboui, Adnen},
title = {Les arrangements minimaux et maximaux d'hyperplans dans $ {\mathbb{P}}^{n}({\mathbb{F}}_{q})$},
journal = {Comptes Rendus. Math\'ematique},
pages = {287--290},
publisher = {Elsevier},
volume = {344},
number = {5},
year = {2007},
doi = {10.1016/j.crma.2007.01.006},
language = {fr},
url = {https://www.numdam.org/articles/10.1016/j.crma.2007.01.006/}
}
TY - JOUR
AU - Rodier, François
AU - Sboui, Adnen
TI - Les arrangements minimaux et maximaux d'hyperplans dans $ {\mathbb{P}}^{n}({\mathbb{F}}_{q})$
JO - Comptes Rendus. Mathématique
PY - 2007
SP - 287
EP - 290
VL - 344
IS - 5
PB - Elsevier
UR - https://www.numdam.org/articles/10.1016/j.crma.2007.01.006/
DO - 10.1016/j.crma.2007.01.006
LA - fr
ID - CRMATH_2007__344_5_287_0
ER -
%0 Journal Article
%A Rodier, François
%A Sboui, Adnen
%T Les arrangements minimaux et maximaux d'hyperplans dans $ {\mathbb{P}}^{n}({\mathbb{F}}_{q})$
%J Comptes Rendus. Mathématique
%D 2007
%P 287-290
%V 344
%N 5
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.crma.2007.01.006/
%R 10.1016/j.crma.2007.01.006
%G fr
%F CRMATH_2007__344_5_287_0
Rodier, François; Sboui, Adnen. Les arrangements minimaux et maximaux d'hyperplans dans $ {\mathbb{P}}^{n}({\mathbb{F}}_{q})$. Comptes Rendus. Mathématique, Volume 344 (2007) no. 5, pp. 287-290. doi: 10.1016/j.crma.2007.01.006
[1] On the number of solutions of polynomial systems, Finite Fields Appl., Volume 3 (1997) no. 4, pp. 287-299
[2] On the number of points of some hypersurfaces in , Finite Fields Appl., Volume 2 (1996) no. 2, pp. 214-224
[3] The packing problem in statistics, coding theory and finite projective spaces: update 2001, Finite Geometries, Developments in Mathematics, vol. 3, Kluwer, Boston, 2001, pp. 201-246
[4] The parameters of projective Reed–Muller codes, Discrete Math., Volume 81 (1990) no. 2, pp. 217-221
[5] A. Sboui, Second highest number of points of hypersurfaces in , à paraître dans Finite Fields Appl. (2005)
[6] Special numbers of rational points on hypersurfaces in the n-dimensional projective space over a finite field http://iml.univ-mrs.fr/... (soumis au J. Algebraic Geom., novembre 2006, disponible sur Internet à l'adresse)
[7] Lettre à M. Tsfasman, Astérisque, Volume 198–199–200 (1991), pp. 351-353
[8] Projective Reed–Muller codes, IEEE Trans. Inform. Theory, Volume 37 (1991) no. 6, pp. 1567-1576
Cited by Sources:





