报告题目：Linear Codes from Boolean Functions with High (Fast) Algebraic Immunity

报告人：唐春明 研究员 西华师范大学

报告时间：2021年4月21日 9:30 - 10:30

报告地点：理科楼B1202

主持人：李成举

报告摘要：In the talk, we propose a new parameter to measure the resistance of a Boolean function to fast algebraic attack. We also introduce the notion of fast immunity profile and show that it informs both on the resistance to standard and fast algebraic attacks. Further, a coding-theory approach to the characterization of perfect algebraic immune functions is presented. Via this characterization, infinite families of binary linear complementary dual codes (or LCD codes for short) are obtained from perfect algebraic immune functions. Moreover, two methodologies for constructing minimal binary codes from sets, Boolean functions and vectorial Boolean functions with high algebraic immunity, are proposed. More precisely, a general construction of new minimal codes using minimal codes contained in Reed-Muller codes and sets without nonzero low degree annihilators is presented. The other construction allows us to yield minimal codes from certain subcodes of Reed-Muller codes and vectorial Boolean functions with high algebraic immunity.

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院长、研究员。2012年博士毕业于北京大学。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。主要研究密码、编码及其相关的数学理论。近年来在线性码、LCD码、密码函数、组合设计等领域做出了一系列突出成果。先后主持国家自然科学基金青年项目和面上项目各一项，获得教育部高等学校科学研究优秀成果奖自然科学类二等奖一项。发表研究论文60余篇，其中SCI、EI检索论文50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》。曾访问多所国内外知名院校；目前担任三个国际期刊的编委。