In [U. Dempwolff: \textit{More Translation Planes and Semifields from Dembowski-Ostrom Polynomials}, Designs, Codes, Cryptogr. \textbf{68} (1-3) (2013), 81--103] three classes of rank two presemifields of order $q^{2n}$, with $q$ and $n$ odd, were exhibited, leaving as an open problem the isotopy issue. In [M. Lavrauw, G. Marino, O. Polverino, R. Trombetti: \textit{Solution to an isotopism question concerning rank 2 semifields}, J. Comb. Des., \textbf{23} (2015), 60--77], the authors faced with this problem answering the question whether these presemifields are new for $n>3$. In this paper we complete the study solving the case $n=3$.
The isotopism problem of a class of 6-dimensional rank 2 semifields and its solution
MARINO, Giuseppe;POLVERINO, Olga;
2015
Abstract
In [U. Dempwolff: \textit{More Translation Planes and Semifields from Dembowski-Ostrom Polynomials}, Designs, Codes, Cryptogr. \textbf{68} (1-3) (2013), 81--103] three classes of rank two presemifields of order $q^{2n}$, with $q$ and $n$ odd, were exhibited, leaving as an open problem the isotopy issue. In [M. Lavrauw, G. Marino, O. Polverino, R. Trombetti: \textit{Solution to an isotopism question concerning rank 2 semifields}, J. Comb. Des., \textbf{23} (2015), 60--77], the authors faced with this problem answering the question whether these presemifields are new for $n>3$. In this paper we complete the study solving the case $n=3$.File in questo prodotto:
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