Geodesic
On sets of vectors of a finite vector space in which every subset of basis size is a basis
Journal of the European Mathematical Society, Tome 14 (2012) no. 3, pp. 733-748.

Voir la notice de l'article provenant de la source EMS Press

It is shown that the maximum size of a set S of vectors of a k-dimensional vector space over Fq​, with the property that every subset of size k is a basis, is at most q+1, if k≤p, and at most q+k−p, if q≥k≥p+1≥4, where q=ph and p is prime. Moreover, for k≤p, the sets S of maximum size are classified, generalising Beniamino Segre's “arc is a conic'' theorem.
DOI : 10.4171/jems/316
Classification : 51-XX, 05-XX, 15-XX, 94-XX
Keywords: Arcs, Maximum Distance Separable Codes (MDS codes), uniform matroids 
@article{JEMS_2012_14_3_a3,
     author = {Simeon Ball},
     title = {On sets of vectors of a finite vector space in which every subset of basis size is a basis},
     journal = {Journal of the European Mathematical Society},
     pages = {733--748},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2012},
     doi = {10.4171/jems/316},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/316/}
}
TY  - JOUR
AU  - Simeon Ball
TI  - On sets of vectors of a finite vector space in which every subset of basis size is a basis
JO  - Journal of the European Mathematical Society
PY  - 2012
SP  - 733
EP  - 748
VL  - 14
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/316/
DO  - 10.4171/jems/316
ID  - JEMS_2012_14_3_a3
ER  - 
%0 Journal Article
%A Simeon Ball
%T On sets of vectors of a finite vector space in which every subset of basis size is a basis
%J Journal of the European Mathematical Society
%D 2012
%P 733-748
%V 14
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/316/
%R 10.4171/jems/316
%F JEMS_2012_14_3_a3
Simeon Ball. On sets of vectors of a finite vector space in which every subset of basis size is a basis. Journal of the European Mathematical Society, Tome 14 (2012) no. 3, pp. 733-748. doi : 10.4171/jems/316. http://geodesic.mathdoc.fr/articles/10.4171/jems/316/

Cité par Sources :