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)  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.
|Journal||Finite Fields and Their Applications|
|Publication status||Published - 2010|
- Scattered linear set