主 讲 人 ：Denis S. Krotov    首席研究员

活动时间：2025-06-05 19:00:00

地      点 ：理科群1号楼D203室 https://us06web.zoom.us/j/86763384947?pwd=qXhOzOcHvaaiw2jqADI8iqNavdgm14.1 会议 ID: 86763384947；密码: 612593

主办单位：数学科学学院

讲座内容：

A partition of the vertices of a graph is called equitable if, for all cells $A$ and $B$ of the partition, the vertices from $A$ have a constant number of neighbors in $B$. In Cayley graphs on the additive group of a small vector space over a finite field $\mathrm{GF}(q)$ of order $q = 2$ or $q = 3$, we look for completely regular (CR) codes whose parameters are new in Hamming graphs over the same field.

The existence of a CR code in such a Cayley graph $G$ implies the existence of a CR code with the same parameters in the corresponding Hamming graph that covers $G$. This way, we find several completely regular codes with new parameters in Hamming graphs over $\mathrm{GF}(3)$. The most interesting findings are two new CR-$1$ codes (namely, CR-codes with covering radius $1$) that are independent sets and one new CR-$2$ code.

By recursive constructions, every new CR code induces an infinite sequence of CR codes (in particular, optimal orthogonal arrays if the original code is CR-$1$ and

independent). In between, we classify feasible parameters of CR codes in several

strongly regular graphs.

主讲人介绍：

Denis S. Krotov received his bachelor's and master's degrees in mathematics from Novosibirsk State University (Russia) in 1995 and 1997, respectively. He earned his Ph.D. and Dr.Sc. degrees in discrete mathematics and theoretical cybernetics from the Sobolev Institute of Mathematics (Novosibirsk, Russia) in 2000 and 2011, respectively. Since 1997, he has been affiliated with the Theoretical Cybernetics Department at the Sobolev Institute of Mathematics, where he currently holds the position of Chief Researcher.

In 2003, he was a Visiting Researcher at the Pohang University of Science and Technology (South Korea). Between 2018 and 2023, he visited Anhui University (China) for several months as a Foreign Expert, and since 2024 he has been a Visiting Researcher at Hebei Normal University (Hebei province, China). His research interests include topics in algebraic combinatorics, coding theory, and graph theory.