Fq-pseudoreguli of PG(3,q3) and scattered semifields of order q6

Michel Lavrauw, Marino Giuseppe, Olga Polverino, Rocco Trombetti

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In this paper, we study rank two semifields of order q6 that are of scattered type. The known examples of such semifields are some Knuth semifields, some Generalized Twisted Fields and the semifields recently constructed in Marino et al. (in press) [12] for . Here, we construct new infinite families of rank two scattered semifields for any q odd prime power, with ; for any q=22h, such that and for any q=h3 with . Both the construction and the proof that these semifields are new, rely on the structure of the linear set and the so-called pseudoregulus associated to these semifields.
Original languageEnglish
Pages (from-to)225-239
JournalFinite Fields and Their Applications
Volume17
Issue number3
Publication statusPublished - 2010

Keywords

  • Semifield
  • Scattered linear set
  • Pseudoregulus

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