题目：Quadratic Forms and Their Applications in Coding Theory

报告人：唐春明 研究员 （西南交通大学）

摘要：Quadratic forms play a pivotal role in various branches of mathematics, including number theory and algebra, and have profound applications in coding theory. In this talk, we explore the theory of quadratic forms over finite fields and their significant impact on the construction and analysis of codes. Specifically, we examine the use of quadratic forms in generating self-orthogonal codes, which are essential in the development of quantum codes, lattice theory, and linear complementary dual (LCD) codes. By leveraging quadratic forms over finite fields, we construct new families of ternary self-orthogonal codes with flexible parameters. We rigorously analyze the parameters of these codes, demonstrating their minimal nature and their few nonzero weight characteristics, with at most five nonzero weights. The methods and results discussed in this talk offer a novel approach to constructing self-orthogonal codes with applications extending to quantum information processing and error-correction schemes.

报告人 简介：唐春明，研究员，西南交通大学信息科学与技术学院。2012年7月获得北京大学博士学位，先后在巴黎第八大学与香港科技大学从事博士后研究工作，方向为面向网络空间安全的编码理论。以独立/第一/通讯作者身份在领域权威期刊发表论文70余篇，包括编码理论最顶级期刊IEEE Transactions on Information Theory 28篇。荣获国际学术奖：布尔奖（George Boole Prize）；研究成果也曾获教育部自然科学二等奖（排名2/4）；主持国家自然科学基金重点项目和面上项目。

报告时间：2024年9月25日15:00-16:00

报告地点：教二楼527

  联系人：张俊