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讲座:The k-Subset Sum Problem over Finite Fields

   主讲人:王维琼

   主讲人工作单位:长安大学

   时间:2019年4月19日 9:00

   地点:科学楼204(三创中心)

   主讲人简介:王维琼,博士,长安大学理学院教授。从事《复变函数与积分变换》、《高等数学》、《线性代数》、《密码学》等课程的教学工作,以及数论、编码理论与密码学的研究工作。在首届全国高校数学微课程教学设计竞赛中获全国特等奖;在第二届全国高校教师微课竞赛中获全国一等奖;在陕西高等学校第二届青年教师讲课竞赛中获陕西省一等奖。主持并完成国家自然科学基金青年基金项目一项陕西省科技计划面上项目一项公开发表学术论文二十余篇。 

   讲座主要内容:The subset sum problem is an important theoretical problem with many applications, such as in coding theory, cryptography, graph theory and some other fields. One of the many aspects of this problem is to answer the solvability of the k-subset sum problem, which has been proven to be NP-hard in general. However, if the evaluation set has some special algebraic structure, it is possible to obtain some good conclusions. We provide in this talk a sufficient condition for the solvability of k-subset sum problem by using estimates on additive character sums over the subset of Fq. We then use this conclusion to deal with the solvability of the k-subset sum problem over two specific known examples of subsets of Fq . Furthermore, we present an explicit combinatorial formula for the number of k-subset sums of quadratic residues over finite fields.

   组织单位:数学与金融学院