报告题目：Wei’s Duality for Generalized Poset Weight over Galois Ring

报告人：曹喜望教授，南京航空航天大学

报告时间：2025年11月18日（周二）14:00

报告地点：20-200

报告摘要：Wei’s duality theorem, proposed by Wei in 1991, initially deals with the generalized Hamming weight (GHW) of linear codes over finite fields. Specifically, the Wei’s duality theorem describes the relationship between the GHWs of a linear code and those of its dual code. The GHWs of linear codes are important parameters for measuring the security of codes in certain cryptographic applications. In this talk, we will generalize the concept of GHW of linear codes over finite fields to the generalized poset weight (GPW) of linear codes over Galois rings. We also present an extension of GPW, abbreviated as EGPW. Similar to the GHWs, we derive two forms of the Wei’s duality theorem with respect to GPWs and EGPWs. In conclusion, we demonstrate that the GPWs of linear codes serve as indicators for assessing the security of information transmission within the wire-tap channel of type II. This is a joint work with Ying Wang and Gaojun Luo.

报告人简介：曹喜望，南京航空航天大学理学院教授，博士生导师。于北京大学获得博士学位。研究方向是有限域及其应用，在图论、差集、指数和、有限域上的多项式、量子信息处理以及代数编码方面做出了出色的工作，其研究成果发表在相关领域的权威期刊IEEE Transaction on Information Theory、Finite Fields and their Applications、Design Codes and Cryptography、Science China（Mathematics）等上，发表学术论文200余篇，出版专著1部。曹喜望教授曾先后多次访问悉尼大学、韩国高等研究中心、南洋理工大学、香港科技大学、北京国际数学研究中心等。2010年入选江苏省“青蓝工程”学术带头人。主持完成国家自然科学基金项目6项和省部级科研项目多项。2017年获得江苏省科学技术奖。