报告题目 (Title)：关于不可约循环码的置换自同构群（ON THE PERMUTATION AUTOMORPHISM GROUPS OF IRREDUCIBLE CYCLIC CODES）
报告人 (Speaker)：向青 教授（南方科技大学）
报告时间 (Time)：2026年3月18日(周三) 10:30
报告地点 (Place)：校本部F309
邀请人(Inviter)：张红莲
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 paper, 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.
This classification has several consequences. First, it yields a general description of non-standard linear recurring sequence subgroups, extending the earlier work of Brison and Nogueira; secondly it establishes the Schmidt-White conjecture for all non-standard irreducible cyclic codes. Moreover, our results provide strong evidence in support of the conjecture of Berger and Charpin that almost all cyclic codes are standard.