报告题目：基于线性码的3-设计及2-设计构造

报 告 人：许广魁（淮南师范学院副教授）

报告时间：2022年3月25日（星期五），14;00-16:00

报告地点：腾讯会议ID：165 127 002；会议密码：123456

报告摘要：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 as to whether there exists?an infinite family of near MDS codes holding an infinite family of?t-designs for t≥2. ??This paper is ?devoted to ?the construction of ?infinite families of 3-designs and?2-designs from special equations over finite fields. First, we present an infinite family of almost MDS codes over GF(p^m) ???holding an infinite family of 3-designs. We then provide an infinite family of almost MDS codes over GF(p^m) ??holding an infinite family of 2-designs ?for any field GF(q). In particular, ?some of these almost MDS codes are ?near MDS.?Second, we present an infinite family of near MDS codes over 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.

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科学研究部

数学科学学院

2022年3月21日

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报告人简介：许广魁，淮南师范学院副教授，博士，国防科技大学博士后，安徽省教坛新秀。主要从事有限域及其应用、代数编码研究。主持国家自然科学基金项目2项、安徽省自然科学基金项目1项、安徽省高校自然科学研究重点项目1项、安徽高校优秀青年人才支持计划重点项目1项，在《IEEE Transactions on Information Theory》《Finite Fields and Their Applications》《Discrete mathematics》等国内外重要学术期刊上发表学术论文20余篇，其中SCI检索15余篇。