Report Title：The Permutation Automorphism Groups of Irreducible Cyclic Codes
Reporter：Qing Xiang
Affiliation: Southern University of Science and Technology
Report Time:10:00-12:00， May 18, 2026
Report Location:Fifth Seminar Room, Mathematics Building
Abstract:
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.
Bio:
Xiang Qing is a Distinguished Professor and current Chair of the Department of Mathematics at Southern University of Science and Technology. His main research interests include combinatorial design, finite geometry, coding theory, extremal combinatorics and additive combinatorics. He has published over 100 academic papers in top-tier international journals such as *Advances in Mathematics*, *Transactions of the American Mathematical Society*, as well as leading combinatorial journals including *Journal of Combinatorial Theory Series A*, *Journal of Combinatorial Theory Series B* and *Combinatorica*. In 1999, he was awarded the Kirkman Medal by the Institute of Combinatorics and its Applications. He has presided over more than ten research projects including grants from the US National Science Foundation, overseas and Hong Kong & Macao cooperative projects and key programs funded by the National Natural Science Foundation of China. He has delivered over 60 plenary and invited talks at international academic conferences.
