Fq-pseudoreguli of PG(3,q3) and scattered semifields of order q6

Authors:
Michel Lavrauw;Giuseppe Marino;Olga Polverino;Rocco Trombetti
Affiliations:
Department of Mathematics, University of Ghent, 9000-Ghent, Belgium;Dipartimento di Matematica, Seconda Universití degli Studi di Napoli, I-81100 Caserta, Italy;Dipartimento di Matematica, Seconda Universití degli Studi di Napoli, I-81100 Caserta, Italy;Dipartimento di Matematica e Applicazioni, Universití degli Studi di Napoli "Federico II", I-80126 Napoli, Italy
Venue:
Finite Fields and Their Applications
Year:
2011

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Abstract

In this paper, we study rank two semifields of order q^6 that are of scattered type. The known examples of such semifields are some Knuth semifields, some Generalized Twisted Fields and the semifields recently constructed in Marino et al. (in press) [12] for q=1(mod3). Here, we construct new infinite families of rank two scattered semifields for any q odd prime power, with q=1(mod3); for any q=2^2^h, such that h=1(mod3) and for any q=3^h with h@?0(mod3). Both the construction and the proof that these semifields are new, rely on the structure of the linear set and the so-called pseudoregulus associated to these semifields.