报告题目：Perfect codes in Doob schemes: linear, additive, and unrestricted.

报 告 人：Denis Krotov教授（俄罗斯科学院）

报告时间：2020年12月17号（周四）下午16:00-18:00

报告地点：腾讯会议 ID：764 179 063 

报告摘要：Doob schemes D(m,n) are metric association schemes with the same algebraic parameters as the Hamming scheme H(2m+n)=D(0,2m+n). The distance-1 graph of D(m,n) is the direct product of m copies of the Shrikhande graph of order 16 and n copies of the complete graph of order 4. The points of the scheme can be associated with a module over the Galois ring GR(4^2) os order 16, and a code is called linear (additive) if it is a submodule (respectively, a subgroup of the additive group). We study the problem of the existence and the characterization of 1-perfect codes in Doob schemes. Linear perfect codes are characterized up to equivalence, while additive and unrestricted 1-perfect codes are characterized up to parameters. In some Doob graphs, only unrestricted 1-perfect codes exist, while for some parameters m, n there are additive, but not linear 1-perfect codes. The talk is based on the material in three papers, one of them is a joint work with Minjia Shi and Daitao Huang.

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数学科学学院

2020年12月17日

报告人简介：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.