报告题目：Binary Linear Codes from Vectorial Boolean Functions and their Weight Distribution

主 讲 人：唐 灯

单 位：上海交通大学网络空间安全学院

时 间：9月2日15:00

腾 讯 ID：437 987 391

密 码：123456

摘 要：

Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this talk, we introduce several classes of binary linear codes from vectorial Boolean functions and determine their parameters, by further studying a generic construction developed by Ding et al. recently. First, by employing perfect nonlinear functions and almost bent functions, we obtain several classes of six-weight linear codes which contain the all-one codeword, and determine their weight distribution. Second, we investigate a subcode of any linear code mentioned above and consider its parameters. When the vectorial Boolean function is a perfect nonlinear function or a Gold function in odd dimension, we can completely determine the weight distribution of this subcode. Besides, our linear codes have larger dimensions than the ones by Ding et al.'s generic construction.

简 介：

唐灯，上海交通大学长聘教轨副教授、博士生导师。2015年3月毕业于法国巴黎第八大学，获应用数学博士学位。主要研究方向为密码函数设计、对称密码分析、代数编码及其应用、分布式存储与计算。在国内外重要学术期刊和学术会议发表研究论文三十余篇，含第一通讯作者IEEE Transactions on Information Theory、Designs, Codes and Cryptography、SIAM Journal on Discrete Mathematics、Cryptography and Communications期刊论文十余篇。主持国家自然科学基金青年科学基金项目、国家自然科学基金面上项目、密码科学技术国家重点实验室开放课题、装备预研重点实验室基金项目等。先后获得IEEE成都分会2014年最佳学生论文奖、中国密码学会2019年密码算法学术会议最佳论文奖、全国密码算法设计竞赛分组密码算法三等奖。