Some new examples of derived semifield planes with affine elations (Q1184578)

To construct derived semifield planes \textit{N. Biliotti} and \textit{G. Menichetti} [J. Geom. 19, 50-88 (1982; Zbl 0529.51006)] have described a class of semifields which are called \(BM\)-semifields in the paper under review. Such semifields \(Q\) are two dimensional right vector spaces over a field \(K\) with a biadditive map \(d: Q\to K\) with some additional properties. In this paper the author gives some new examples of such semifields in which \(K=GF(2^ 3)\) or \(K=GF(2^ 4)\). With the help of a computer all possible maps \(d\) in the first case are given. One of the three maps belongs to a new class of semifields. In the case \(K=GF(2^ 4)\) only necessary conditions for new examples are given by the computer.