We construct six new infinite families of finite semifields, all of which are two-dimensional over their left nuclei. We give constructions for both even and odd characteristics when the left nucleus has odd dimension over the center. The characteristic is odd in the one family in which the left nucleus has even dimension over the center. Spread sets of linear maps are used in all the constructions.
Infinite families of New Semifields / Ebert, G. L.; Marino, G.; Polverino, O.; Trombetti, Rocco. - In: COMBINATORICA. - ISSN 0209-9683. - STAMPA. - 29:6(2009), pp. 637-663. [10.1007/s00493-009-2406-5]
Infinite families of New Semifields
MARINO G.;TROMBETTI, ROCCO
2009
Abstract
We construct six new infinite families of finite semifields, all of which are two-dimensional over their left nuclei. We give constructions for both even and odd characteristics when the left nucleus has odd dimension over the center. The characteristic is odd in the one family in which the left nucleus has even dimension over the center. Spread sets of linear maps are used in all the constructions.File in questo prodotto:
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