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 q2n, 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 DA and DAB, are new for n>3, whereas presemifields in family DB are isotopic to Generalized Twisted Fields for each n≥3.
| Original language | English |
|---|---|
| Pages (from-to) | 60-77 |
| Number of pages | 18 |
| Journal | Journal of Combinatorial Designs |
| Volume | 23 |
| Issue number | 2 |
| Publication status | Published - 2015 |
Keywords
- isotopism
- semifields