Maximum scattered linear sets of pseudoregulus type and the Segre variety S n,n

In this paper we study a family of scattered F q -linear sets of rank tn of the projective space PG ( 2 n − 1 ,q t ) ( n ≥ 1, t ≥ 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.

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