Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	周悦研究员，国防科技大学
Inviter:	陈绍示
Title:	On the construction and the equivalence of maximum scattered linear sets
Language:	Chinese
Time & Venue:	2023.08.11 15:00-16:00 思源楼525
Abstract:	The concept of linear sets in projective spaces was introduced by Lunardon in 1999 and it plays central roles in the study of blocking sets, semifields, rank-metric codes and etc. A linear set with the largest possible cardinality and maximum rank is called maximum scattered. Despite of two decades of study, there are only three known families of maximum scattered linear sets defined over PG(1,q^n) for infinitely many n. The first family is called pseudo-regulus type by Blokhuis and Lavrauw in 1999. The second family was found by Lunardon and Polverino in 2001 and later generalized by Sheekey in 2016. The third family was constructed by Longobardi, Marino, Trombetti and the speaker recently. In this talk, we first summarize the known methods for the construction of maximum scattered linear sets in PG(1,q^n). Then we turn to the equivalence problem of them. In particular, we consider the automorphism groups of the known maximum scattered linear sets.