Lunardon, G.; Marino, G.; Polverino, O.; Trombetti, R.
Maximum scattered linear sets of pseudoregulus type and the Segre variety $\mathcal{S}_{n,n}$
Journal of Algebraic Combinatorics 39(4), 807-831 (2014)
DOI: 10.1007/s10801-013-0468-3
Summary
In this paper we study a family of scattered $\mathbb{F}_{q}$-linear sets of rank $tn$ of the projective space $PG(2n-1,q^t)(n\geq 1,t\geq 3)$, called of pseudoregulus type, generalizing results contained in Lavrauw and van de Voorde, Des. Codes Crypt. 20(1) (2013) and in Marino et al. J. Combin. Theory, Ser. A 114:769-788 (2007). As an application, we characterize, in terms of the associated linear sets, some classical families of semifields: the Generalized Twisted Fields and the 2-dimensional Knuth semifields.
