Institute of Mathematics and Informatics

Семинар “Problems and Methods Related to Coding Theory“
2021-03-30 13:00 - 14:30 (Europe/Sofia) | Zoom
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.
Join Zoom Meeting
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Zoom ID: 851 9342 8253
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Семинар “Problems and Methods Related to Coding Theory“
2021-03-02 13:00 - 14:30
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 codes that attain the bounds are found in terms of the parameters of Levenshtein-type quadrature formulas. Necessary and sufficient conditions for the optimality of our bounds are derived. Further, we obtain upper bounds on the energy of codes of fixed minimum and maximum distances and cardinality.
Joint work with Peter Dragnev, Douglas Hardin, Edward Saff, Maya Stoyanova
Страница на семинара: http://www.math.bas.bg/moiuser/PMCT/
ТеТ
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Zoom ID: 910 5863 2644
Password: [REDACTED]
https://zoom.us/j/91058632644?pwd=[REDACTED]
