Abstract
In this paper, elaborating on the link between semifields of dimension n over their left nucleus and \({\mathbb{F}s}\)-linear sets of rank en disjoint from the secant variety \({\Omega(\mathcal{S}_{n,n})}\) of the Segre variety \({\mathcal{S}_{n,n}}\) of \({PG(n^2-1, q), q=s^e}\), we extend some operations on semifield whose definition relies on dualising the relevant linear set.
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This work was supported by the Research Project of MIUR (Italian Ministry for University and Research): “Strutture Geometriche, Combinatoria e loro Applicazioni” and by the Research group GNSAGA of INDAM.
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Lunardon, G., Marino, G., Polverino, O. et al. The Generalized Translation Dual of a Semifield. Ann. Comb. 21, 629–643 (2017). https://doi.org/10.1007/s00026-017-0362-0
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DOI: https://doi.org/10.1007/s00026-017-0362-0