论文标题
两个最大散射线性家族的等效性和自身形态组
Equivalence and automorphism groups of two families of maximum scattered linear sets
论文作者
论文摘要
在有限场上的射影空间中的线性集合在阻塞集，半场，排名码码等的研究中扮演着核心角色。等线性可能的基数最大，最大等级称为最大散布。尽管进行了二十年的研究，但投影线中只有少数已知的最大散射线性集，包括由Csajbók，Marino，Polverino和Zanella 2018建造的家庭，以及由Csajbók，Marino，Zullo，Zullo 2018（也是Marino，Montanucci和Zullo 2020）建造的家庭。本文旨在解决每个家庭中线性集的等效问题，并确定其自动形态群体。
Linear set in projective spaces over finite fields plays central roles in the study of blocking sets, semifields, rank-metric codes and etc. A linear set with the largest possible cardinality and the maximum rank is called maximum scattered. Despite two decades of study, there are only a few number of known maximum scattered linear sets in projective lines, including the family constructed by Csajbók, Marino, Polverino and Zanella 2018, and the family constructed by Csajbók, Marino, Zullo 2018 (also Marino, Montanucci, and Zullo 2020). This paper aims to solve the equivalence problem of the linear sets in each of these families and to determine their automorphism groups.
