两类最大散射线性集的等价性与自同构群  

Equivalence and automorphism groups of two families of maximum scattered linear sets

作　　者：唐薇 周悦[1] Wei Tang;Yue Zhou

机构地区：[1]国防科技大学理学院,长沙410073

出　　处：《中国科学：数学》2023年第2期279-300,共22页Scientia Sinica：Mathematica

基　　金：湖南省自然科学基金(批准号:2019RS2031);长沙市杰出创新青年培养计划(批准号:kq2106006)资助项目。

摘　　要：有限域上射影空间中的线性集在阻碍集、半域和秩度量码等的研究中起着核心作用.具有最大可能的元素个数和最大秩的线性集称为最大散射线性集.经过近20年的研究,目前已知的射影直线上最大散射线性集的个数仍然较少,其中包含Csajbók等(2018)和Marino等(2020)构造的两类.本文旨在解决这两类最大散射线性集中每一类中元素的等价问题,并确定它们的自同构群.Linear set in projective spaces over finite fields plays central roles in the study of blocking sets,semifields and rank-metric codes.A linear set with the largest possible cardinality and the maximum rank is called maximum scattered.After two decades of study,there are only a small number of known maximum scattered linear sets in projective lines,including two types constructed by Csajbók et al.(2018)and Marino et al.(2020).This paper aims to solve the equivalence problem of the linear sets in each of these families and to determine their automorphism groups.

关 键 词：线性集 秩距离码 有限几何 线性多项式 

分 类 号：O152[理学—数学] O174.14[理学—基础数学]