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} [...]

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, която ще се проведе онлайн на 02 март 2021 г. от 13:00 часа. Петър Бойваленков, ИМИ-БАН, ще изнесе доклад на тема: Universal Bounds for Cardinality and Energy of Codes of Given Minimum and Maximum Distances Abstract. We employ signed measures that are positive definite up to certain degrees to establish Levenshtein-type upper bounds on the cardinality of codes with given minimum and maximum distances, and universal lower bounds on the potential energy (for absolutely monotone interactions) for codes with given maximum distance and cardinality. The distance distributions of [...]