Abstract：

Difference sets (DS) are basic and important structures in combinatorial design theory. Many generalizations and variants of DS have been proposed and extensively studied during the past 50 years; these generalizations include partial difference sets (PDS), difference families (DF), and external difference families (EDF). Some generalizations and variants of DS arise directly from their applications.

External difference families (EDF) and circular EDF (CEDF) were introduced by D.R. Stinson et al. in 2004 and 2023, respectively, for the purpose of cryptographic applications. In this talk we will present old and new results on constructions and (non)existence of EDF's and CEDF 's. We will also mention a few open problems in this area in the end of the talk.

About the speaker：

Keqin Feng is a mathematician with broad interests, especially in algebra, coding theory, cryptography, and number theory. He is currently an emeritus professor of Tsinghua University. Keqin Feng received the M.S. degree from the University of Science and Technology of China (USTC), Beijing, China, in 1968, and had been a professor at USTC and Tsinghua University. He got the S.S. Chern Prize of the Chinese Mathematical Society in 1991, and the L.K. Hua Prize of the Chinese Mathematical Society (the lifetime achievement award), in 2019.