报 告 人：Denis Krotov 教授
工作单位：Sobolev Institute of Mathematics
Denis Krotov received the Bachelor’s degree in Mathematics in 1995 and the Master’s degree in 1997, both from Novosibirsk State University, the Ph.D. and Dr.Sc. degrees in Discrete Mathematics and Theoretical Cybernetics from Sobolev Institute of Mathematics, Novosibirsk, in 2000 and 2011, respectively. Since 1997, he has been with Theoretical Cybernetics Department, Sobolev Institute of Mathematics, where he is currently a Chief Researcher. In 2003, he was a visiting researcher with Pohang University of Science and Technology, Korea. His research interest includes subjects related to algebraic combinatorics, coding theory, and graph theory.
This talk is a survey of recent results about the construction and the characterization of some classes of optimal codes in the Doob metric schemes, which have the same algebraic parameters as the quaternary Hamming metric scheme. We consider the characterization of parameters of perfect codes (linear, additive, and unrestricted), characterization of the MDS codes, and MacWilliams theorems.