In [G. Marino, O. Polverino, R. Trombetti, On Fq-linear sets of PG(3,q3) and semifields, J. Combin. Theory Ser. A 114 (5) (2007) 769–788] it has been proven that there exist six non-isotopic families Fi (i=0,...,5)ofsemifieldsoforderq6withleftnucleusFq3 andcenterFq,accordingtothedifferentgeo- metric configurations of the associated Fq -linear sets. In this paper we first prove that any semifield of order q6 with left nucleus Fq3 , right and middle nuclei Fq2 and center Fq is isotopic to a cyclic semifield. Then, we focus on the family F4 by proving that it can be partitioned into three further non-isotopic families: F (a) , F (b) , F (c) and we show that any semifield of order q 6 with left nucleus F 3 , right and middle nuclei 444 q F 2 and center Fq belongs to the family F(c). q4 © 2007 Elsevier Inc. All rights reserved.
Semifields of order q^6 with left nucleus F_{q^3} and center F_q / Johnson, N. L.; Marino, G; Polverino, O; Trombetti, Rocco. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - STAMPA. - 14:(2008), pp. 456-469. [10.1016/j.ffa.2007.04.005]
Semifields of order q^6 with left nucleus F_{q^3} and center F_q
MARINO G;TROMBETTI, ROCCO
2008
Abstract
In [G. Marino, O. Polverino, R. Trombetti, On Fq-linear sets of PG(3,q3) and semifields, J. Combin. Theory Ser. A 114 (5) (2007) 769–788] it has been proven that there exist six non-isotopic families Fi (i=0,...,5)ofsemifieldsoforderq6withleftnucleusFq3 andcenterFq,accordingtothedifferentgeo- metric configurations of the associated Fq -linear sets. In this paper we first prove that any semifield of order q6 with left nucleus Fq3 , right and middle nuclei Fq2 and center Fq is isotopic to a cyclic semifield. Then, we focus on the family F4 by proving that it can be partitioned into three further non-isotopic families: F (a) , F (b) , F (c) and we show that any semifield of order q 6 with left nucleus F 3 , right and middle nuclei 444 q F 2 and center Fq belongs to the family F(c). q4 © 2007 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
