Permutation codes, secure codes and hash families related to extremal and probabilistic combinatorics

活动时间： 05月21日09时40分       

地            点  ： 理科群1号楼D-203室

讲座内容：

A code can be regarded as a subset of its underlying base set satisfying some restrictions. In this talk, we will discuss the bounds and constructions for several classes of combinatorial codes, which are closely related to extremal and probabilistic combinatorics. These codes include: permutation codes, separable codes, frameproof codes and some related hash families for security protection. For the lower bounds, by regarding a code as an independent set of a graph or a hypergraph, we are able to improve the known lower bounds for permutation codes, 3-perfect hash families, 2- frameproof codes and ¯2-separable codes. In addition, we extend the constructions for separable codes and frameproof codes by applying the probabilistic method. Particularly, we obtain asymptotically optimal ¯2-separable codes by the deletion method. For the upper bounds, by considering some typical configurations of codes and applying combinatorial counting skills, we are able to improve the known upper bounds for separable codes and frameproof codes. Furthermore, using a result of Erd˝os and Gallai on hypergraph matching, we approve partially a well-known conjecture on an old problem of the disjunctive code theory.

主讲人介绍：

葛根年，教育部“长江学者奖励计划”特聘教授、国家杰出青年科学基金获得者、“新世纪百千万人才工程”国家级人选。1996年6月在苏州大学获博士学位，1996年8月至2001年8月在苏州大学任教，2001年9月至2002年8月在加拿大CONCORDIA大学从事博士后研究工作，2002年9月至2004年2月在美国VERMONT大学任访问助理教授。2004年3月回国，在浙江大学任教授、博士生导师。2013年3月调入首都师范大学工作。长期从事组合设计理论及其应用研究，具体内容涉及：组合设计理论、编码密码学、信号处理、计算机科学、生物信息学和统计学等领域。迄今在《Journal of Combinatorial Theory, Series A》、《SIAM Journal on Discrete Mathematics》、《IEEE Transactions on Information Theory》、《IEEE Transactions on Signal Processing》、《Mathematics of Computation》等国内外重要期刊上发表学术论文155篇，其中：SCI收录141篇、SCI引用1150余次、当前H指数（h-index）为18。

发布时间：2015-05-18 09:15:44