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A binary code is called a superimposed cover-free (s, ℓ)-code if the code is identified by the incidence matrix of a family of finite sets in which no intersection of ℓ sets is covered by the union of s others. A binary code is called a superimposed list-decoding s L-code if the code is identified by the incidence matrix of a family of finite sets in which… (More)

A binary code is said to be a disjunctive list-decoding s L-code, s ≥ 1, L ≥ 1, (briefly, LD s L-code) if the code is identified by the incidence matrix of a family of finite sets in which the union of any s sets can cover not more than L − 1 other sets of the family. In this paper, we introduce a natural probabilistic generalization of LD s L-code when the… (More)

A binary code is called a superimposed cover-free $(s,\ell)$-code if the code is identified by the incidence matrix of a family of finite sets in which no intersection of $\ell$ sets is covered by the union of $s$ others. A binary code is called a superimposed list-decoding $s_L$-code if the code is identified by the incidence matrix of a family of finite… (More)

We discover some important properties of cover-free (CF) codes, separating system (SS) codes and completely separating system (CSS) codes connected with the concept of constant weight CF codes. New upper and lower bounds on the rate of CF codes, SS codes and CSS codes based on the known results for CF codes are obtained. Tables of numerical values for the… (More)

Let 1 ≤ s < t, N ≥ 1 be integers and a complex electronic circuit of size t is said to be an s-active, s ≪ t, and can work as a system block if not more than s elements of the circuit are defective. Otherwise, the circuit is said to be an s-defective and should be substituted for the s-active circuit. Suppose that there exists a possibility to check the… (More)

In the given article we generalize a construction presented in [3]. We give a method of constructing a cover-free (s, ℓ)-code. For k > s, our construction yields a (n s) ℓ × n k cover-free (s, ℓ)-code with a constant column weight. Let N , t, s and ℓ be integers, where 1 ≤ s < t and 1 < ℓ < t − s. Let denote the equality by definition, |A| – the size of the… (More)

—Learning a hidden hypergraph is a natural generalization of the classical group testing problem that consists in detecting unknown hypergraph Hun = H(V, E) by carrying out edge-detecting tests. In the given paper we focus our attention only on a specific family F(t, s, ℓ) of localized hypergraphs for which the total number of vertices |V | = t, the number… (More)

Learning a hidden hypergraph is a natural generalization of the classical group testing problem that consists in detecting unknown hypergraph Hun = H(V, E) by carrying out edge-detecting tests. In the given paper we focus our attention only on a specific family F(t, s, ℓ) of localized hypergraphs for which the total number of vertices |V | = t, the number… (More)

Let 1 ≤ s < t, N ≥ 1 be integers and a complex electronic circuit of size t is said to be an s-active, s ≪ t, and can work as a system block if not more than s elements of the circuit are defective. Otherwise, the circuit is said to be an s-defective and should be replaced by a similar s-active circuit. Suppose that there exists a possibility to run N… (More)

Group testing is a well known search problem that consists in detecting up to s defective elements of the set [t] = {1,. .. , t} by carrying out tests on properly chosen subsets of [t]. In classical group testing the goal is to find all defective elements by using the minimal possible number of tests. In this paper we consider multistage group testing. We… (More)