报告题目：The Permutation Automorphism of Irreducible Cyclic Codes
腾讯会议：721-354-407   4月13日 下午14：30-15：30

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 {\bf F}$_q$ is called irreducible if its check polynomial is irreducible over {\bf F}$_q$. 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.

个人简介：向青，现任南方科技大学讲席教授，深耕组合设计、有限几何、编码理论和加法组合领域多年，学术造诣深厚。他1995年毕业于俄亥俄州立大学并获博士学位，1999年斩获国际组合数学及其应用协会颁发的Kirkman奖章，曾先后担任美国加州理工注册送彩金 Bateman Instructor、美国特拉华大学终身教职及浙江大学讲座教授，在相关研究领域享有广泛影响力。

报告题目：The Permutation Automorphism of Irreducible Cyclic Codes
腾讯会议：721-354-407   4月13日 下午14：30-15：30

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 {\bf F}$_q$ is called irreducible if its check polynomial is irreducible over {\bf F}$_q$. 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.

个人简介：向青，现任南方科技大学讲席教授，深耕组合设计、有限几何、编码理论和加法组合领域多年，学术造诣深厚。他1995年毕业于俄亥俄州立大学并获博士学位，1999年斩获国际组合数学及其应用协会颁发的Kirkman奖章，曾先后担任美国加州理工注册送彩金 Bateman Instructor、美国特拉华大学终身教职及浙江大学讲座教授，在相关研究领域享有广泛影响力。

报告题目：The Permutation Automorphism of Irreducible Cyclic Codes
腾讯会议：721-354-407   4月13日 下午14：30-15：30

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 {\bf F}$_q$ is called irreducible if its check polynomial is irreducible over {\bf F}$_q$. 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.

个人简介：向青，现任南方科技大学讲席教授，深耕组合设计、有限几何、编码理论和加法组合领域多年，学术造诣深厚。他1995年毕业于俄亥俄州立大学并获博士学位，1999年斩获国际组合数学及其应用协会颁发的Kirkman奖章，曾先后担任美国加州理工注册送彩金 Bateman Instructor、美国特拉华大学终身教职及浙江大学讲座教授，在相关研究领域享有广泛影响力。