On the automorphism groups of Lunardon-Polverino scattered linear sets
release_pg63fmiqpvfc7kadayg4qyvbi4
by
Wei Tang, Yue Zhou, Ferdinando Zullo
2022
Abstract
Lunardon and Polverino introduced in 2001 a new family of maximum scattered
linear sets in PG(1,q^n) to construct linear minimal Rédei
blocking sets. This family has been extended first by Lavrauw, Marino,
Trombetti and Polverino in 2015 and then by Sheekey in 2016 in two different
contexts (semifields and rank metric codes). These linear sets are called
Lunardon-Polverino linear sets and this paper aims to determine its
automorphism group, to solve the equivalence issue among Lunardon-Polverino
linear sets and to establish the number of inequivalent linear sets of this
family. We then elaborate on this number, providing explicit bounds and
determining its asymptotics.
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