报告题目：Construction of MDS Euclidean Self-Dual Codes

报告专家：周海燕 南京师范大学 教授

报告时间：2025年03月22日（周六）上午09:00-10:00

报告地点：腾讯会议 会议ID：972 324 949

报告摘要：Euclidean self-dual codes have also been found various interesting applications in many aspects. It is of great interest to investigate the MDS Euclidean self-dual codes. Note that a q-ary MDS Euclidean self-dual code of length n has dimension n/2 and minimum distance n + 1. So it is sufficient to consider the problem for which lengths an MDS Euclidean self-dual code over finite fields exists. In this report, constructions of MDS Euclidean self-dual codes are presented.

专家简介：周海燕，南京师范大学数学科学学院教授，副院长，博士生导师，曾任国家自然科学基金委数学处流动项目主任，曾访问英国剑桥大学，美国加州大学尔湾分校，加拿大麦克马斯特大学，意大利ICTP，香港科技大学等国内外高校和科研机构，从事代数数论及其应用方面的研究，已在J. Number Theory, Acta Arith., J. Pure Appl. Algebra, Finite Fields and Their Appl.上发表论文三十多篇，主持国家自然科学基金项目多项。

报告题目：Recursive Constructions for Subspace Designs

报告专家：周君灵 北京交通大学 教授

报告时间：2025年03月22日（周六）上午10:00-11:00

报告地点：腾讯会议 会议ID：972 324 949

报告摘要：This talk concentrates on recursive constructions for subspace t-designs. In 1998, Itoh presented a powerful recursive construction: for certain index \lambda, if there exists a Singer cycle invariant 2-(l, 3, \lambda)_q design, then there also exists an SL(m, q^l) invariant 2-(ml,3,\lambda)_q design for all integers m >3. We investigate the GL(m, q^l)-incidence matrix between 2-subspaces and k-subspaces of GF(q)^ml with m >2 and k >3 in this work. As a generalization of Itoh's construction, the important case of m=2 is supplemented and a doubling construction is established for 2-(l, 3, \lambda)_q designs over finite fields. As a further generalization, a product construction is developed for q-analogs of group divisible designs (q-GDDs). For general block dimension k >3, several new infinite families of q-GDDs are constructed. As applications, plenty of new infinite families of subspace 2-designs are constructed. This talk also involves our recent results on recursive constructions for subspace t-designs where t=2, 3 and the block dimension equals 4.

专家简介：周君灵，北京交通大学三级教授、博士生导师，中国运筹学会图论组合分会常务理事。从事组合学与编码理论的研究，主要研究具有特殊性质的三元系大集、互不相交的t-设计、线性码与组合设计、子空间设计与向量空间的极值问题等，发表SCI检索论文60余篇。参与完成国家自然科学基金重点项目，现主持国家自然科学基金面上项目、北京市自然科学基金面上项目。