The seminar on

Problems and Methods Related to Coding Theory

organized by:

Department of Mathematical Foundations of Informatics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria

Novosibirsk State University, Novosibirsk, Russia

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

is inviting you to its next meeting.

Assist. Prof. Ivan Mogilnykh,

Novosibirsk State University,

will deliver a talk on:

Completely regular codes in Johnson and Grassmann graphs

Abstract. Completely regular codes in Johnson and Grassmann graph are interrelated with t-designs. In this talk we give an introduction to these codes and discuss several old and recent results. Martin noted that any (k-1)-(n,k,1)-design D is a completely regular code in the Johnson graph J(n,k). Avgustinovich and Mogilnykh showed that {B:|B|=k+1, B does not contain any blocks of D} is a completely regular code in J(n,k+1).

We prove that when D is the Steiner quadruple system of the extended Hamming code of length n one can obtain the following completely regular code in J(n,6): {B:|B|=6, B does not contain any blocks of D}.

Analogous ideas yield a completely regular code in Grassmann graph Jq(n,4) from Desarguesian line spread.

Website of the seminar: http://www.math.bas.bg/moiuser/PMCT/

The seminar will be held on March 30, 2021 (Tuesday), at 1:00 p.m.

Join Zoom Meeting

https://us02web.zoom.us/j/85193428253?pwd=NzIycEVQb0NEMzFReVE1aTVOU3JWQT09
Zoom ID: 851 9342 8253
Passcode: 970063