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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)

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)

—We discuss upper and lower bounds of zero error capacity for signature coding models based on the symmetric noiseless multiple access channel. set of integers from 1 to N and |A| – the size of the set A. A q-nary (N × t)-matrix t q (1) with t columns (codewords) x(j), j ∈ [t], and N rows x i , i ∈ [N ], is called a q-nary code of length N and size t = q RN… (More)

Let 1 ≤ s < t, N ≥ 1 be fixed 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)

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)

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)