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The seminar on

Problems and Methods Related to Coding Theory

organized by:

Novosibirsk State University, Novosibirsk, Russia

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

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria

is inviting you to its next meeting to be held on March 2, 2021 at 1 p.m.

Prof. Peter Boyvalenkov,

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

will deliver a talk on:

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

Time: March 2, 2021, 13:00 Sofia (18:00 Novosibirsk, 14:00 Moscow) Zoom ID: 910 5863 2644
Password: 12624120

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