Solution to an isotopism question concerning rank 2 semifields
Combinatorics
2013-05-21 v1
Abstract
In [U. Dempwolff: More Translation Planes and Semifields from Dembowski-Ostrom Polynomials, Designs, Codes, Cryptogr. \textbf{68} (1-3) (2013), 81-103], the author gives a construction of three classes of rank two semifields of order , with and 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 , in particular we prove that two of these classes, labeled and , are new for , whereas presemifields in family are isotopic to Generalized Twisted Fields for each .
Keywords
Cite
@article{arxiv.1305.4342,
title = {Solution to an isotopism question concerning rank 2 semifields},
author = {Michel Lavrauw and Giuseppe Marino and Olga Polverino and Rocco Trombetti},
journal= {arXiv preprint arXiv:1305.4342},
year = {2013}
}