On the automorphism groups of Lunardon-Polverino scattered linear sets release_pg63fmiqpvfc7kadayg4qyvbi4

by Wei Tang, Yue Zhou, Ferdinando Zullo

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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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Date   2022-01-30
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arXiv  2201.12777v1
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