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报告题目：Infinite families of linear codes supportingt-designs

主讲人：周君灵

报告时间：2024年5月18日11:00-11:30

报告地点：西安电子科技大学南校区网安大楼12楼A-1236

主讲人介绍：

周君灵，北京交通大学三级教授、博士生导师，中国运筹学会图论组合分会常务理事、编码密码与相关组合理论分会理事。从事组合学与编码理论的研究，在柯克曼三元系大集、单纯或可分解有向三元系大集、互不相交的t-设计、线性码与组合设计、光正交码等方面的研究中取得了丰富成果，发表SCI检索论文60余篇。参与完成国家自然科学基金重点项目，现主持国家自然科学基金面上项目、北京市自然科学基金面上项目。

报告主要观点：

Tang and Ding [IEEE IT 67 (2021) 244-254] studied the class of BCH codes   and their dual codes with and established that the codewords of the minimum (or the second minimum) weight in these codes support  4-designs or 3-designs. Motivated by this, we further investigate the codewords of the next adjacent weight in such codes and discover more  infinite classes of t-designs with t=3,4. In particular, we prove that  codewords of weight 7 in   support 4-designs for odd m5  and they support 3-designs for even m4, which provide infinite classes of simple t-designs with new parameters. Another significant class of t-designs  we produce has complementary designs with parameters 4-(+ 1,5,5); these designs have the smallest  index among all the known simple 4-(q+1,5,) designs derived from codes for prime powers q; and they are further proved to be isomorphic to the 4-designs admitting the projective general linear group PGL(2,) as the automorphism group constructed by Alltop in 1969.