Solution to An Isotopism Question Concerning Rank 2 Semifields

Authors


  • 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.

Abstract

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

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