题目：Infinite families of 3-designs and 2-designs from almost MDS codes

主讲人：曹喜望

时间：2022年04月27日09:00-10:00

地址：腾讯会议ID：702-380-433

摘要：Combinatorial designs are closely related to linear codes. Recently, some near MDS codes were employed to construct $t$-designs by Ding and Tang, which settles the question regarding whether there exists an infinite family of near MDS codes holding an infinite family of $t$-designs for $t \geq 2$. In this talk, I will introduce some constructions of infinite families of 3-designs and 2-designs from special equations over finite fields. First, I will present an infinite family of almost MDS codes over $ {\rm GF}(p^m)$ holding an infinite family of 3-designs. Then I will provide an infinite family of almost MDS codes over $ {\rm GF}(p^m)$ holding an infinite family of 2-designs for any field ${\rm GF}(q)$. In particular, some of these almost MDS codes are near MDS. Second, I will present an infinite family of near MDS codes over ${\rm GF}(2^m)$ holding an infinite family of 3-designs by considering the number of roots of a special linearized polynomial. Compared to previous constructions of 3-designs or 2-designs from linear codes, the parameters of some of our designs are new and flexible. This is a joint work with Guangkui Xu and Longjiang Qu.

主讲人简介：曹喜望，南京航空航天大学理学院教授，博士生导师。北京大学获得博士学位。研究方向是有限域及其应用，在差集、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，发表学术论文130余篇。曹喜望教授先后多次访问过Sydney大学、南洋理工大学，香港科技大学、台湾中央研究院、北京国际数学中心、南开大学陈省身数学研究所等。2010年入选江苏省“青蓝工程”学术带头人，主持国家自然科学基金面上项目和省部级科研项目多项。2017年获得江苏省科学技术奖。

邀请人：胡思煌

审核人：魏普文