Speaker: 李伟聪助理教授，大湾区大学

Inviter: 陈绍示（中国科学院数学与系统科学研究院系统科学研究所）

Title: On the automorphism group of irreducible cyclic codes

Language: Chinese

Time & Venue: 2025.11.05 13:30-14:30 思源楼525

Abstract: The study of permutation automorphism groups of cyclic codes is a central problem in algebraic coding theory. An irreducible cyclic code—one defined by an irreducible check polynomial—is termed standard if its permutation group is generated solely by the cyclic shift and the Frobenius automorphism; otherwise, it is non-standard. In this talk, I will present recent results that characterize these groups for irreducible cyclic codes. We show that the non-standard case is exceptional, as most of these codes are, in fact, standard. The proof leverages a detailed analysis of the subgroup structure of general linear groups. This is joint work with Tao Feng, Henk Hollmann, and Qing Xiang.