报告时间：2020年12月24日 10:00—11:00
报告地点：红瓦楼723
报告人简介：许扬 博士后
本科，2008-2012，复旦大学数学科学学院，数学与应用数学专业。
博士，2012-2017，复旦大学数学科学学院，基础数学方向。
博士后，2017-现在，复旦大学计算机科学技术学院。
博士后，2018-现在，香港大学理学院数学系。
报告摘要：In $1991$, Wei proved a duality theorem that established an interesting connection between the generalized Hamming weights of a linear code and those of its dual code. Wei's duality theorem has since been extensively studied from different perspectives and extended to other settings. In this talk, we re-examine Wei's duality theorem and its various extensions, henceforth referred to as Wei-type duality theorems, from a new Galois connection perspective. Our approach is based on the observation that the generalized Hamming weights and the dimension/length profiles of a linear code form a Galois connection. Our main result is a general Wei-type duality theorem for two Galois connections between finite subsets of $\mathbb{Z}$, from which all the known Wei-type duality theorems can be recovered. As corollaries of the main result, we prove new Wei-type duality theorems for some combinatorial notions, and we further unify and generalize all the known Wei-type duality theorems established for codes endowed with various metrics.