Solution to an isotopism question concerning rank 2 semifields

Michel Lavrauw, Marino Giuseppe, Olga Polverino, Rocco Trombetti

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

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 languageEnglish
Pages (from-to)60-77
Number of pages18
JournalJournal of Combinatorial Designs
Volume23
Issue number2
Publication statusPublished - 2015

Keywords

  • isotopism
  • semifields

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