A Steiner triple system (STS) contains a transversal subdesign TD(3, w) if its point set has three pairwise disjoint subsets A, B, C of size w and w2 blocks of the STS intersect with each of A, B, C (those w2 blocks form a TD(3,w)). We prove several structural properties of Steiner triple systems of order 3w + 3 that contain one or more transversal subdesigns TD(3, w). Using exhaustive search, we find

We describe the construction of a piecewise polynomial generator over a Galois ring and prove a transitivity criterion for it. We give an estimate for the discrepancy of the output sequences of such a generator. We show that the obtained estimate is asymptotically equivalent to known estimates for special cases of a piecewise polynomial generator, and in some cases it is asymptotically sharper.

We consider q-ary block codes with exactly two distances: d and d + 1. Several constructions of such codes are given. In the linear case, we show that all codes can be obtained by a simple modification of linear equidistant codes. Upper bounds for the maximum cardinality of such codes are derived. Tables of lower and upper bounds for small q and n are presented.

Orthogonal arrays play an important role in statistics and experimental design. Like other combinatorial constructions, the most important and studied problems are questions about their existence and classification. An essential step to solving such problems is determination of Hamming distance distributions of an orthogonal array with given parameters. In this paper we propose an algorithm for computing

We consider the problem of finding maximum values of f-divergences Df(P ∥ Q) of discrete probability distributions P and Q with values on a finite set under the condition that the variation distance V(P, Q) between them and one of the distributions P or Q are given. We obtain exact expressions for such maxima of f-divergences, which in a number of cases allow to obtain both explicit formulas and upper

We study the maximum remaining service time in M(2)∣G2∣∞ fork -join queueing systems where an incoming task forks on arrival for service into two subtasks, each of them being served in one of two infinite-sever subsystems. The following cases for the arrival rate are considered: (1) time-independent, (2) given by a function of time, (3) given by a stochastic process. As examples of service time distributions

We establish an extended large deviation principle for processes with independent and stationary increments on the half-line under the Cramer moment condition in the space of functions of bounded variation without discontinuities of the second kind equipped with the Borovkov metric.

This paper concerns the folklore statement that “entropy is a lower bound for compression.” More precisely, we derive from the entropy theorem a simple proof of a pointwise inequality first stated by Ornstein and Shields and which is the almost-sure version of an average inequality first stated by Khinchin in 1953. We further give an elementary proof of the original Khinchin inequality, which can be

We consider the moving element search problem with the minimum total cardinality of tests. As a search space, we consider the set of integer points of a segment of length n. We prove that the total test cardinality of an asymptotically optimal adaptive strategy is \(n + 2\sqrt n \).

By a (Latin) unitrade of order k, we call a subset of vertices of the Hamming graph H(n, k) that intersects any maximal clique at either 0 or 2 vertices. A bitrade is a bipartite unitrade, i.e., a unitrade that can be split into two independent subsets. We study the cardinality spectrum of bitrades in the Hamming graph H(n, k) with k = 3 (ternary hypercube) and the growth of the number of such bitrades

We refine a lower bound on the spectrum of a binary code. We give a simple derivation of the known bound on the undetected error probability of a binary code.

For any channel, the existence of a unique Augustin mean is established for any positive order and probability mass function on the input set. The Augustin mean is shown to be the unique fixed point of an operator defined in terms of the order and the input distribution. The Augustin information is shown to be continuously differentiable in the order. For any channel and convex constraint set with

We derive an analog of the Frankl-Wilson theorem on independence numbers of some distance graphs. The obtained results are applied to the problem of the chromatic number of a space ℝn with a forbidden equilateral triangle and to the problem of chromatic numbers of distance graphs with large girth.

We present a family of easily computable upper bounds for the Holevo (information) quantity of an ensemble of quantum states depending on a reference state (as a free parameter). These upper bounds are obtained by combining probabilistic and metric characteristics of the ensemble. We show that an appropriate choice of the reference state gives tight upper bounds for the Holevo quantity which in many

We consider the problem of finding the maximum values of divergences D(P‖Q) and D(Q‖P) for probability distributions P and Q ranging in the finite set \(\mathcal{N}=\left\{1,\;2,...,n\right\}\) provided that both the variation distance V (P,Q) between them and either the probability distribution Q or (in the case of D(P‖Q)) only the value of the minimal component qmin of the probability distribution

We slightly improve the superconcentrator construction by Alon and Capalbo.

We consider alphabetic coding of superwords. We establish an unambiguity coding criterion for the cases of finite and infinite codes. We prove that in the case of an infinite code the ambiguity detection problem is m-complete in the ∃1∀0 class of Kleene’s analytical hierarchy.

A quarter century ago Chor, Fiat, and Naor proposed mathematical models for revealing a source of illegal redistribution of digital content (tracing traitors) in the broadcast encryption framework, including the following two combinatorial models: nonbinary IPP codes, based on an (n, n)-threshold secret sharing scheme, and IPP set systems, based on the general (w, n)-threshold secret sharing scheme

Cyclic codes as a subclass of linear codes have practical applications in communication systems, consumer electronics, and data storage systems due to their efficient encoding and decoding algorithms. The objective of this paper is to construct some cyclic codes by the sequence approach. More precisely, we determine the dimension and the generator polynomials of three classes of q-ary cyclic codes

Abstract—We correct mistakes in the formulations of Theorem 19 and Proposition 17 of the original article, published in vol. 55, no. 1, 1–45.