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报告题目：On Infinite Families of Narrow-Sense Antiprimitive BCH Codes Admitting 3-Transitive Automorphism Groups

报告人：唐春明 研究员（ 西南交通大学）

摘要：The Bose-Chaudhuri-Hocquenghem (BCH) codes are a well-studied subclass of cyclic codes that have found numerous applications in error correction and notably in quantum information processing. They are widely used in data storage and communication systems. A subclass of attractive BCH codes is the narrow-sense BCH codes over the Galois field GF(q) with length q+1, which are closely related to the action of the projective general linear group of degree two on the projective line. Despite its interest, not much is known about this class of BCH codes. In this talk we aim to study some of the codes with in this class and specifically narrow-sense antiprimitive BCH codes (these codes are also linear complementary duals (LCD) codes that have interesting practical recent applications in cryptography, among other benefits).We shall use tools and combine arguments from algebraic coding theory, combinatorial designs, and group theory (group actions, representation theory of finite groups, etc.) to investigate narrow-sense antiprimitive BCH Codes and extend results from the recent literature. Notably, the dimension, the minimum distance of some q-ary BCH codes with length q+1, and their duals are determined. The dual codes of the narrow-sense antiprimitive BCH codes derived include almost MDS codes. Furthermore, the classification of PGL(2,p^m)-invariant codes over GF(p^h) is completed. As an application of this result, the p-ranks of all  in cadence structures invariant under the projective general linear group PGL(2,p^m) are determined. Furthermore, infinite families of narrow-sense BCH codes admitting a 3- transitive automorphism group are obtained. Via these BCH codes, a coding theory approach to constructing the Witt spherical geometry designs is presented. The BCH codes proposed in this talk are good candidates for permutation decoding, as they have a relatively large group of automorphisms.  

报告人简介：唐春明，1982年，西南交通大学信息科学与技术学院研究员。2012年7月获得北京大学博士学位，先后在巴黎第八大学与香港科技大学从事博士后研究工作（海外经历3年：巴黎1年，香港2年），方向为面向网络空间安全的编码密码理论。以独立/第一/通讯作者身份在领域权威期刊发表论文60余篇，包括编码密码理论最顶级期刊IEEE Transactions on Information Theory 20余篇。因在密码函数领域的贡献，荣获密码学国际学术奖：布尔奖（George Boole Prize）；研究成果也曾获教育部自然科学二等奖（排名2/4）；正在主持国家自然科学基金重点项目和面上项目。

报告时间：2023年3月3日（周五）下午16：00-17：00

线下报告地点：校本部教二楼827

联系人：张俊