报告题目：The Permutation Automorphism Groups of Irreducible Cyclic Codes
报 告 人：Qing Xiang
所在单位： Southern University of Science and Technology
报告时间：10:00-12:00， May 18, 2026
报告地点：数学楼第五研讨室
报告摘要: The study of permutation automorphism groups of cyclic codes is a central topic in algebraic coding theory. A cyclic code over Fq is called irreducible if its check polynomial is irreducible over Fq. Such a code is standard if its permutation automorphism group is equal to the group generated by the cyclic shift and the Frobenius automorphism, and non-standard otherwise. In this talk, we give a complete classification of all non-standard non-degenerate irreducible cyclic codes, using the classification of finite simple groups. Our result shows that, apart from a small number of explicit exceptional families and their descendants under certain secondary constructions, every non-degenerate irreducible cyclic code is standard, and up to four explicit exceptions, every degenerate cyclic code is non-standard.
报告人简介：向青为南方科技大学数学系讲席教授, 现任数学系系主任。向青教授的主要研究方向为组合设计、有限几何、编码理论，极值组合和加法组合。在顶尖数学综合期刊《Advances in Math.》，《Trans. AMS》和国际组合数学界最高级别杂志《J. Combin. Theory Ser. A》，《J. Combin. Theory Ser. B》， 《Combinatorica》等重要国际期刊上发表学术论文100余篇。于1999年荣获了国际组合数学及其应用协会颁发的Kirkman奖章。主持完成美国国家自然科学基金、中国自然科学基金海外和港澳合作、中国自然科学基金重点项目等科研项目10余项。曾在国际学术会议上作大会报告或特邀报告60余次。
