Nonbinary perfect codes and tilings

主 讲 人 ：Denis S. Krotov    研究员

活动时间：02月08日15时00分    

地      点 ：腾讯会议：655 918 870,密码：854580

讲座内容：

Atiling $(A,B)$ of a finite vector space $F_q^n$ is a factorization of itsadditive group into the direct sum of two sets: $F_q^n=A+B$, $|F_q^n|=|A||B| $.An $r$-perfect code is a set $C$ forming a tiling together with a ball $B$ ofradius $r$ (it is assumed that the space is equipped with a Hamming metric, anda ball is defined in the natural way). We will discuss the relationship betweentilings and perfect codes, as well as the construction of perfect full-rankcodes using tilings (a code is  full-rank if its affine span isthe whole space).

主讲人介绍：

DenisS. Krotov received the Bachelor’s degree in Mathematics in 1995 and theMaster's degree in 1997, both from Novosibirsk State University, the Ph.D. andDr.Sc. degrees in Discrete Mathematics and Theoretical Cybernetics from SobolevInstitute of Mathematics, Novosibirsk, in 2000 and 2011, respectively. Since1997, he has been with Theoretical Cybernetics Department, Sobolev Institute ofMathematics, where he is currently a Chief Researcher. In 2003, he was avisiting researcher with Pohang University of Science and Technology, Korea.For four months in 2018 and 2019, he visited the Anhui University, China. Hisresearch interest includes subjects related to algebraiccombinatorics, coding theory, and graph theory.

发布时间：2022-02-08 08:22:59