Maximum scattered linear sets of pseudoregulus type and the Segre variety $\mathcal{S}_{n,n}$

By G. Lunardon, G. Marino, Olga Polverino, R. Trombetti. 2012

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In this paper we study a family of scattered $\mathbb{F}_{q}$-linear sets of rank tn of the projective space PG(2n−1,qt) (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.

Subfields: Artificial Intelligence, Computer Networks and Communications, Discrete Mathematics and Combinatorics

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