学  术  报  告  (2019069）

报告题目： On good polynomials over finite fields for optimal locally recoverable codes              

报告人：    Sihem 教授（法国巴黎第八大学）

报告时间：2019年10月26日上午9:00—10:00

报告地点：理学实验楼312

报告摘要： A locally recoverable (LRC) code is a code that enables a simple recovery of an erased symbol by accessing only a small number of other symbols. LRC codes currently form one of the rapidly developing topics in coding theory because of their applications in distributed and cloud storage systems.

In 2014, Tamo and Barg have presented in a very remarkable paper a family of LRC codes that attain the maximum possible (minimum) distance (given code length, cardinality, and locality). The key ingredient for constructing such optimal linear LRC codes is the so-called $r$-good polynomials, where $r$ is equal to the locality of the LRC code. In this talk, we review and discuss new good polynomials over finite fields for constructing optimal LRC codes.

报告人简介： Sihem Mesnager教授本科和博士均毕业于法国巴黎六大，现为法国巴黎八大和巴黎高科国立高等电信学校双聘教授，是实验室LAGA研究团队MTII“信息和图像处理数学”的联合负责人。其主要研究领域为离散数学、对称密码、编码理论、交换代数和计算代数几何。她目前是国际信息与编码理论杂志（IJOCT）的主编，数学与通讯进展（AMC）的联合主编，也是IEEE-IT副主编。已经发表论文120余篇，专著2本。从2016年开始担任法国信息论分会主席。

学  术  报  告  (2019070)

报告题目： Cyclic bent functions and their applications

报告人：    唐春明副教授（西华师范大学）

报告时间：2019年10月26日上午10:00—11:00

报告地点：理学实验楼312

报告摘要： This talk focuses on cyclic bent functions and their applications. The first objective of this talk is to establish a link between quadratic cyclic bent functions and a special type of prequasifields, and construct a class of quadratic cyclic bent functions from the Kantor-Williams prequasifields. The second objective is to use cyclic bent functions to construct mutually unbiased bases (MUBs), optimal codebooks and  optimal sequence families. The third objective is to present a family of binary and quaternary codes containing the standard Kerdock code as a special case, and describe their support designs. It shows that cyclic bent functions have nice applications in several fields such as coding theory, symmetric cryptography, quantum physics, compressed sensing and CDMA communication.

报告人简介：唐春明，男，博士，西华师范大学数学与信息学院副教授。2012年博士毕业于北京大学。并先后在巴黎第八大学和香港科技大学从事博士后研究工作。主要研究包括密码、编码及其相关的数学理论。先后主持国家自然科学基金青年项目和面上项目各一项。发表研究论文 40 余篇，其中EI、SCI 检索论文30 余篇，代表性成果发表在国内外重要学术期刊《IEEE Transactions on Information Theory》、《Finite Fields and Their Applications 》、《Designs, Codes and Cryptography 》、《Science China》和《China Communications》 等上面。曾访问多所国内外知名院校；担任三个国际期刊的编委。