报告题目：Linear Representations of Finite Geometries and Associated LDPC Codes
时 间：2026年3月31日（星期二）08：30
地 点：理工南楼621
主 办：数学与统计学院，分析数学及应用教育部重点实验室，福建省分析数学及应用重点实验室
参加对象：相关专业师生
报告摘要：The linear representation of a subset of a finite projective space is an incidence structure of affine points and lines determined by the subset. In this talk we use character theory to show that the rank of the incidence matrix has a direct geometric interpretation in terms of certain hyperplanes. We consider the LDPC codes defined by taking the incidence matrix and its transpose as parity-check matrices, and in the former case prove a conjecture of Vandendriessche that the code is generated by words of minimum weight called plane words. In the latter case we compute the minimum weight in some cases and provide a few constructions of codewords.
报告人简介：向青，现任南方科技大学讲席教授，深耕组合设计、有限几何、编码理论和加法组合领域多年，学术造诣深厚。他1995年毕业于俄亥俄州立大学并获博士学位，1999年斩获国际组合数学及其应用协会颁发的Kirkman奖章，曾先后担任美国加州理工学院Bateman Instructor、美国特拉华大学终身教职及浙江大学讲座教授，在相关研究领域享有广泛影响力。