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20200713 周悅 Asymptotics of Moore exponent sets

發布時間:2020-07-07 15:59    瀏覽次數:    來源:

題目:Asymptotics of Moore exponent sets
報告人: 周悅,國防科技大學副研究員
時間:2020/07/13  周一  14:30-15:30
騰訊會議 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.

報告人介紹:周悅博士現任國防科技大學數學系副研究員,曾獲德國“洪堡”學者資助,2016年度Kirkman獎章獲得者。在Adv. Math, JCTA等著名期刊上發表SCI論文近30篇,主持國家自然科學基金面上項目1項,青年項目1項,獲湖南省優秀青年基金資助。

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