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講座:The k-Subset Sum Problem over Finite Fields

   主講人:王維瓊

   主講人工作單位:長安大學

   時間:2019年4月19日 9:00

   地點:科學樓204(三創中心)

   主講人簡介:王維瓊,博士,長安大學理學院教授。從事《復變函數與積分變換》、《高等數學》、《線性代數》、《密碼學》等課程的教學工作,以及數論、編碼理論與密碼學的研究工作。在首屆全國高校數學微課程教學設計競賽中獲全國特等獎;在第二屆全國高校教師微課競賽中獲全國一等獎;在陜西高等學校第二屆青年教師講課競賽中獲陜西省一等獎。主持并完成國家自然科學基金青年基金項目一項陜西省科技計劃面上項目一項公開發表學術論文二十余篇。 

   講座主要內容: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.

   組織單位:數學與金融學院


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