Geodesic
Semifields in class \(\mathcal F_{4}^{(a)}\)
The electronic journal of combinatorics, Tome 16 (2009) no. 1
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

The semifields of order $q^6$ which are two-dimensional over their left nucleus and six-dimensional over their center have been geometrically partitioned into six classes by using the associated linear sets in $PG(3,q^3)$. One of these classes has been partitioned further (again geometrically) into three subclasses. In this paper algebraic curves are used to construct two infinite families of odd order semifields belonging to one of these subclasses, the first such families shown to exist in this subclass. Moreover, using similar techniques it is shown that these are the only semifields in this subclass which have the right or middle nucleus which is two-dimensional over the center. This work is a non-trivial step towards the classification of all semifields that are six-dimensional over their center and two-dimensional over their left nucleus.
DOI : 10.37236/142
Classification : 51E15 
@article{10_37236_142,
     author = {Gary Ebert and Giuseppe Marino and Olga Polverino and Rocco Trombetti},
     title = {Semifields in class \(\mathcal {F_{4}^{(a)}\)}},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/142},
     zbl = {1182.51002},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/142/}
}
TY  - JOUR
AU  - Gary Ebert
AU  - Giuseppe Marino
AU  - Olga Polverino
AU  - Rocco Trombetti
TI  - Semifields in class \(\mathcal F_{4}^{(a)}\)
JO  - The electronic journal of combinatorics
PY  - 2009
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/142/
DO  - 10.37236/142
ID  - 10_37236_142
ER  - 
%0 Journal Article
%A Gary Ebert
%A Giuseppe Marino
%A Olga Polverino
%A Rocco Trombetti
%T Semifields in class \(\mathcal F_{4}^{(a)}\)
%J The electronic journal of combinatorics
%D 2009
%V 16
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/142/
%R 10.37236/142
%F 10_37236_142
Gary Ebert; Giuseppe Marino; Olga Polverino; Rocco Trombetti. Semifields in class \(\mathcal F_{4}^{(a)}\). The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/142

Cité par Sources :