Maximum scattered ${\mathbb{F}}_q$-linear sets of $\mathrm{PG}(1,q^4)$

Abstract

There are two known families of maximum scattered ${\mathbb{F}}_q$-linear sets in $PG(1,q^t)$: the linear sets of pseudoregulus type and for $t\ge 4$ the scattered linear sets found by Lunardon and Polverino. For $t=4$ we show that these are the only maximum scattered ${\mathbb{F}}_q$-linear sets and we describe the orbits of these linear sets under the groups $PGL(2,q^4)$ and $P\Gamma L(2,q^4)$.

13 pages

References in corpus (1)

• Classes and equivalence of linear sets in $PG(1,q^n)$

Cited by in corpus (1)

• A new family of MRD codes in ${\mathbb{F}}_q^{2n\times 2n}$ with right and middle nuclei ${\mathbb{F}}_{q^n}$