In this paper, we study rank two semifields of order q6 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, Polverino, Trombetti: Towards the classification of rank 2 semifields 6-dimensional over their center, Des. Codes Cryptogr., 61 (2011), no. 1, 11–29],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^{2h}, 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.
F_q-pseudoreguli of PG(3,q^3) and scattered semifields of order q^6
MARINO, Giuseppe;POLVERINO, Olga;
2011
Abstract
In this paper, we study rank two semifields of order q6 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, Polverino, Trombetti: Towards the classification of rank 2 semifields 6-dimensional over their center, Des. Codes Cryptogr., 61 (2011), no. 1, 11–29],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^{2h}, 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
