Solution to An Isotopism Question Concerning Rank 2 Semifields

In [8] Dempwolff gives a construction of three classes of rank two semifields of order q 2 n , 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 n > 3 , in particular we prove that two of these classes, labeled D A and D A B , are new for n > 3 , whereas presemifields in family D B are isotopic to Generalized Twisted Fields for each n ≥ 3 .