报告名称: Linear Representations of Finite Geometries and Associated LDPC Codes

主办单位：数学与统计学学院

报告专家：向青

专家所在单位：美国特拉华大学

报告时间：2020年5月21日15:00—17:00

报告地点：腾讯会议（会议ID：653 311 852）

专家简介：向青，1995获美国Ohio State University博士学位，现为美国特拉华大学(University of Delaware)教授。主要研究方向为组合设计、有限几何、编码和加法组合。现为国际组合数学界权威期刊《The Electronic Journal of Combinatorics》主编，同时担任SCI期刊《Journal of Combinatorial Designs》、《Designs, Codes and Cryptography》的编委。曾获得国际组合数学及其应用协会颁发的杰出青年学术成就奖—Kirkman Medal。在国际组合数学界最高级别杂志《J. Combin. Theory Ser. A》，《J. Combin. Theory Ser. B》,以及《Trans. Amer. Math. Soc.》，《IEEE Trans. Inform. Theory》等重要国际期刊上发表学术论文90余篇。主持完成美国国家自然科学基金、美国国家安全局等科研项目10余项。曾在国际学术会议上作大会报告或特邀报告50余次。

报告摘要：

The linear representation of a subset of a finite projective space is an incidence system 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 several cases and provide explicit constructions of minimum weight codewords.

邀请人：郑大彬