论文标题
在Lunardon-Polverino散射线性套件的自动形态群体上
On the automorphism groups of Lunardon-Polverino scattered linear sets
论文作者
论文摘要
Lunardon和Polverino在2001年推出了一个新的最大散射线性套件的家族，以$ \ mathrm {pg}（1，q^n）$构建线性最小rédei块集。这个家庭于2015年首先由Lavrauw，Marino，Trombetti和Polverino延长，然后在2016年Sheekey在两种不同的情况下（Semifields and Rank Metric Codes）。这些线性集被称为Lunardon-Polverino线性集，本文旨在确定其自动形态组，以解决Lunardon-Polverino线性集合之间的等价问题，并确定该家族的不相等线性集的数量。然后，我们详细说明了这个数字，提供明确的界限并确定其渐近学。
Lunardon and Polverino introduced in 2001 a new family of maximum scattered linear sets in $\mathrm{PG}(1,q^n)$ 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 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.
