Hadamard matrices and spherical designs

发布时间：2024-06-18 作者：浏览次数：

Speaker:	Professor Patrick Sole	DateTime:	2024年06月22日（周六）上午09:30-10:30
Brief Introduction to Speaker: Patrick Solé 教授是国际著名的代数编码顶级专家，是有限环上编码理论的开拓者与奠基人之一，研究领域包括代数组合、代数图论、代数编码、离散数学、格的构造、模形式等等。目前已在国际著名期刊 Transactions of the American Mathematical Society，IEEE Transaction on Information Theory, Journal of Combinatorial Theory Series A，Journal of Combinatorial Theory Series B, Bulletin of the American Mathematical Society, Journal of Algebra 等发表 200 余篇专业学术论文，在国际学术会议上发表论文 80 余篇，出版学术专著6本。		Place:	6号楼二楼报告厅
Abstract:Hadamard codes over finite rings are explored wrt their covering radius for the chinese euclidean distance. Generalized bent sequences, when they exist, provide a lower bound. Upper bounds are obtained by considering a spherical code attached to Hadamard matrices of Butson type. Under mild hypotheses, this code is spherical 2-design, which yields upper bound on its covering radius on the sphere. This bound, in turn, gives an upper bound on the covering radius of the Hadamard codes.