Infinite families of new semifields

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.

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Correspondence to Gary L. Ebert.

Additional information

This author acknowledges the support of NSA grant H98230-06-1-0071.

This work was supported by the Research Project of MIUR (Italian Office for University and Research) “Strutture geometriche, combinatoria e loro applicazioni” and by the Research group GNSAGA of INDAM.

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Ebert, G.L., Marino, G., Polverino, O. et al. Infinite families of new semifields. Combinatorica 29, 637–663 (2009). https://doi.org/10.1007/s00493-009-2406-5

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Mathematics Subject Classification (2000)

  • 51E15