报告题目：Tight upper bounds on the number of non-zero weights of cyclic codes

主 讲 人：陈博聪 教授

时 间：2023年9月22日（周五）14：30

地 点：腾讯会议（744-915-905）

主办单位：理学院

主讲人简介：

  陈博聪， 2013年于华中师范大学数统学院取得博士学位，导师樊恽教授; 随后在南洋理工大学数学系从事博士后研究，从2015年起担任美国《数学评论》评论员。现为华南理工大学数学学院教授、博士生导师，主要研究领域为代数编码、有限群及其应用。已主持国家自然科学基金面上项目两项和青年项目一项，在IEEE IT, DCC, FFA等代数编码主流期刊上发表学术论文多篇。

摘要：

  Let C be a simple-root cyclic code. In this talk, we find explicit formulas for the number of orbits of certain subgroups of the automorphism group of C on C ∗ = C \ {0}. Consequently, upper bounds on the number of non-zero weights of C are derived and necessary and sufficient conditions for codes meeting the upper bounds are exhibited. Several infinite families of reducible and irreducible cyclic codes meeting the bound are presented, revealing that our bounds are tight. Our main results improves and generalizes some of the results in [Shi, Li, Neri and S´ole, IEEE-TIT, 2019] and [Chen and Zhang, IEEE-TIT, 2023]. This talk is based on joint works with Yuqing Fu, Hongwei Liu and Guanghui Zhang.