Separating codes

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.