报告题目：A generic construction of non-generalized Reed-Solomon MDS codes

报告人：华中师范大学刘宏伟教授

时间：2025年11月14日16:00-17:40

地点：立志楼A422

摘要：Maximum distance separable (MDS) codes are optimal with respect to the singleton bound. The systematic generator matrices of MDS codes contain MDS matrices. MDS matrices are an important element for the design of block ciphers such as the AES. Generalized Reed-Solomon (GRS) codes form the most prominent class of MDS codes. There are codes that are MDS but not GRS, which are called non-GRS MDS codes. It is an interesting research filed to provide a general construction for non-GRS MDS codes. Roth and Lemple (1989) constructed non-GRS MDS codes via extending GRS codes. Beelen et al. (2017) introduced twisted Reed-Solomon codes, and showed that families of such codes are non-GRS MDS codes. Recently, there are many research papers focusing on the constructions of non-GRS codes. In this talk, we provide a generic construction of MDS codes, yielding infinitely many examples. We then explicit families of non-GRS MDS codes. Finally, we prove that some of the constructed non-GRS MDS codes are generalized twisted Reed-Solomon (GTRS) codes. This is joint work with Shengwei Liu, Frederique Oggier.

刘宏伟：华中师范大学数学与统计学学院教授，博导，非线性分析及其应用教育部重点实验室副主任，中国工业与应用数学学会第八届理事会理事，中国工业与应用数学学会编码密码及相关组合理论专业委员会委员。主要从事代数编码的研究和教学工作，主持和参与国家自然科学基金多项，973子项目1项，教育部留学回国人员科研启动基金1项。在IEEE Trans. Inf. Theory, Des. Codes Cryptogr., Finite Fields Appl., Discrete Math., Sci. China Math., Cryptogr. Commun.等国内外知名期刊发表相关研究论文70余篇. 合作编写编著教材、著作4部。