English

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 q2nq^{2n}, with qq and nn 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>3n>3, in particular we prove that two of these classes, labeled DAD_{A} and DABD_{AB}, are new for n>3n>3, whereas presemifields in family DBD_{B} are isotopic to Generalized Twisted Fields for each n3n\geq 3.

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}
}
R2 v1 2026-06-22T00:18:44.714Z