廖群英: An improvement for error-correcting pairs of some special MDS codes

报告时间：2024年4月12日（星期五）8:00-9:00 报告地点：翡翠湖校区科教楼B1710室 报 告 人：廖群英 教授 工作单位：四川师范大学 举办单位：数学学院 报告简介： The error-correcting pair is a general algebraic decoding method for linear codes. Since every linear code is contained in an MDS linear code with the same minimum distance over some finite field extensions, we focus on MDS linear codes. Recently, He and Liao showed that for an MDS linear code C with minimum distance 2ℓ + 2, if it has an ℓ-error-correcting pair, then the parameters of the pair have three possibilities. Moreover, for the first case, they gave a necessary condition for an MDS linear code C with minimum distance 2ℓ + 2 to have an ℓ-error-correcting pair, and for the other two cases, they only gave some counterexamples. For the second case, in this talk, we give a necessary condition for an MDS linear code C with minimum distance 2ℓ + 2 to have an ℓ-error-correcting pair, and then basing on the Product Singleton Bound, we prove that there are two cases for such pairs, and then give some counterexamples basing on twisted generalized Reed-Solomon codes for these cases. 报告人简介： 廖群英，四川师范大学数学科学学院，教授，博士生导师，川大博士，清华大学博士后，主要从事编码密码学的数学理论问题研究。