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Solution to An Isotopism Question Concerning Rank 2 Semifields


  • Contract grant sponsor: Research Foundation Flanders- Belgium; contract grant sponsor: Universita’ di Padova; contract grant number: CPDA113797/11; contract grant sponsor: Italian Office for University and Research; contract grant sponsor: Research group GNSAGA of INDAM.


In [8] Dempwolff gives a construction of three classes of rank two semifields of order inline image, 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 inline image, in particular we prove that two of these classes, labeled inline image and inline image, are new for inline image, whereas presemifields in family inline image are isotopic to Generalized Twisted Fields for each inline image.

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