On the automorphism groups of Lunardon-Polverino scattered linear sets

Wei Tang; Yue Zhou; Ferdinando Zullo

On the automorphism groups of Lunardon-Polverino scattered linear sets

Combinatorics 2022-10-10 v2

Authors: Wei Tang , Yue Zhou , Ferdinando Zullo

Abstract

Lunardon and Polverino introduced in 2001 a new family of maximum scattered linear sets in $\mathrm{PG}(1,q^n)$ to construct linear minimal R\'edei 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 their automorphism groups, 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.

Keywords

scattered linear sets automorphism groups lunardon-polverino reedei blocking sets rank metric codes equivalence

Cite

@article{arxiv.2201.12777,
  title  = {On the automorphism groups of Lunardon-Polverino scattered linear sets},
  author = {Wei Tang and Yue Zhou and Ferdinando Zullo},
  journal= {arXiv preprint arXiv:2201.12777},
  year   = {2022}
}

Comments

In the 2nd version, Eq.(15) in Theorem 3.2 has been corrected for even q and odd n

On the automorphism groups of Lunardon-Polverino scattered linear sets

Abstract

Keywords

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