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Principle Seminar of the Department of Probability Theory, Moscow State University
September 21, 2016 16:45, Moscow, MSU, auditorium 12-24
 


Separating codes

I. V. Vorob'ev

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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Abstract: A binary code of length $N$ and size $t$ is said to be a separating $(s, l)$-code if it is an incidence matrix of a family of $t$ subsets of an $N$-set where for every two disjoint sets of subsets of a family $S$ and $L$ with cardinalities $s$ and $l$ there is an element of the original $N$-set such that either it belongs to every subset from S and doesn't belong to any subset from $L$, or it belongs to every subset from $L$ and doesn't belong to any subset from $S$. The purpose of this dissertation is to establish new asymptotic lower and upper bounds on the maximal cardinality $t(N, s, l)$ of binary separating $(s, l)$-codes and their generalization called $q$-ary separating $(s, l)$-codes, which are used in automata theory, digital fingerprinting and some other applied problems of information theory and coding theory.

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