Solution to An Isotopism Question Concerning Rank 2 Semifields |
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| Authors: | Michel Lavrauw Giuseppe Marino Olga Polverino Rocco Trombetti |
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| Institution: | 1. Department of Management and Engineering, Università di Padova, Italy;2. Dipartimento di Matematica e Fisica, Seconda Università degli Studi di Napoli, Italy;3. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Italy |
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| Abstract: | In 8] Dempwolff gives a construction of three classes of rank two semifields of order  , with q and n odd, using Dembowski–Ostrom polynomials. The question whether these semifields are new, i.e. not isotopic to previous constructions, is left as an open problem. In this paper we solve this problem for  , in particular we prove that two of these classes, labeled  and  , are new for  , whereas presemifields in family  are isotopic to Generalized Twisted Fields for each  . |
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| Keywords: | semifield semifield plane linear set |
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