Семинарът 

Problems and Methods Related to Coding Theory,

организиран от

ИМИ – БАН, Секция “Математически основи на информатиката”,

 Novosibirsk State University, Novosibirsk, Russia, и

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

Ви кани на поредната си сбирка, на която

Assist. Prof. Ivan Mogilnykh, Novosibirsk State University,

ще изнесе доклад на тема:

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.

Страница на семинара: http://www.math.bas.bg/moiuser/PMCT/

 Семинарът ще се проведе онлайн на 30 март (вторник) 2021 г. от 13:00 часа.

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