题目：Asymptotics of Moore exponent sets
报告人： 周悦，国防科技大学副研究员
时间：2020/07/13 周一 14：30-15：30
腾讯会议 ID：690 594 700
摘要：Let n be a positive integer and I a k-subset of integers in [0, n − 1]. Given a k-tuple A = (α0,···,αk−1) ∈ Fkqn, let MA,I denote the matrix (αqj) with
i 0≤i≤k−1andj∈I. WhenI={0,1,···,k−1},MA,I iscalled a Moore matrix which was introduced by E. H. Moore in 1896. It is well known that the determinant of a Moore matrix equals 0 if and only if α0, · · · , αk−1 are Fq-linearly dependent. We call I that satisfies this property a Moore exponent set. In fact, Moore exponent sets are equivalent to maximum rank-distance (MRD) code with maximum left and right idealisers over finite fields. It is already known that I = {0, · · · , k − 1} is not the unique Moore exponent set, for instance, (generalized) Delsarte-Gabidulin codes and the MRD codes recently discovered in [2] both give rise to new Moore exponent sets.
By using algebraic geometry approach, we obtain an asymptotic classifica- tion result: for q > 5, if I is not an arithmetic progression, then there exist an integer N depending on I such that I is not a Moore exponent set provided that n > N.
This talk is based on two recent joint works [1] with Daniele Bartoli and [2] with Bence Csajb ́ok, Giuseppe Marino and Olga Polverino.
References：
[1] D. Bartoli and Y. Zhou. Asymptotics of Moore exponent sets. Journal of Combinatorial Theory, Series A, 175:105281, 2020.
[2] B. Csajb ́ok, G. Marino, O. Polverino, and Y. Zhou. MRD codes with maximum idealizers. Discrete Mathematics, 343(9):111985, 2020.
报告人介绍：周悦博士现任国防科技大学数学系副研究员，曾获德国“洪堡”学者资助，2016年度Kirkman奖章获得者。在Adv. Math, JCTA等著名期刊上发表SCI论文近30篇，主持国家自然科学基金面上项目1项，青年项目1项，获湖南省优秀青年基金资助。
