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Geometric Interpretation of Entropy for Dyck Systems Probl. Inf. Transm. (IF 1.34) Pub Date : 20220711
G. D. DvorkinWe consider a relation between the metric entropy and the local boundary deformation rate (LBDR) in the symbolic case. We show the equality between the LBDR understood as a limit almost everywhere and the entropy for a vast class of measures on Dyck systems.

Large Deviation Principle for Terminating Multidimensional Compound Renewal Processes with Application to Polymer Pinning Models Probl. Inf. Transm. (IF 1.34) Pub Date : 20220711
A. V. Logachov, A. A. Mogulskii, E. I. ProkopenkoWe obtain a large deviations principle for terminating multidimensional compound renewal processes. We also obtain the asymptotics of large deviations for the case where a Gibbs change of the original probability measure takes place. The random processes mentioned in the paper are widely used in polymer pinning models.

Entropy in Thermodynamics and in Information Theory Probl. Inf. Transm. (IF 1.34) Pub Date : 20220711
V. A. ZorichWe discuss the relation between the concepts of entropy in thermodynamics and in information theory.

Theoretical and Experimental Upper and Lower Bounds on the Efficiency of Convolutional Codes in a Binary Symmetric Channel Probl. Inf. Transm. (IF 1.34) Pub Date : 20220711
A. A. Kurmukova, F. I. Ivanov, V. V. Zyablov 
Poissonian TwoArmed Bandit: A New Approach Probl. Inf. Transm. (IF 1.34) Pub Date : 20220711
A. V. Kolnogorov 
On the Maximum Number of NonConfusable Strings Evolving under Short Tandem Duplications Probl. Inf. Transm. (IF 1.34) Pub Date : 20220711
M. KovačevićThe set of all \(q\)ary strings that do not contain repeated substrings of length \({\le\! 3}\) (i.e., that do not contain substrings of the form \(a a\), \(a b a b\), and \(a b c a b c\)) constitutes a code correcting an arbitrary number of tandemduplication mutations of length \({\le\! 3}\). In other words, any two such strings are nonconfusable in the sense that they cannot produce the same string

On New Problems in Asymmetric Cryptography Based on ErrorResistant Coding Probl. Inf. Transm. (IF 1.34) Pub Date : 20220711
V. V. Zyablov, F. I. Ivanov, E. A. Krouk, V. R. SidorenkoWe consider the problem of constructing a cryptosystem with a public key based on errorresistant coding. At present, this type of cryptosystems is believed to be able to resist the advent of quantum computers and can be considered as a method of postquantum cryptography. The main drawback of a codebased cryptosystem is a great length of the public key. Most papers devoted to reducing the cryptosystem

Bounds on Threshold Probabilities for Coloring Properties of Random Hypergraphs Probl. Inf. Transm. (IF 1.34) Pub Date : 20220410
A. S. Semenov, D. A. ShabanovWe study the threshold probability for the property of existence of a specialform \(r\)coloring for a random \(k\)uniform hypergraph in the \(H(n,k,p)\) binomial model. A parametric set of \(j\)chromatic numbers of a random hypergraph is considered. A coloring of hypergraph vertices is said to be \(j\)proper if every edge in it contains no more than \(j\) vertices of each color. We analyze

On qary Propelinear Perfect Codes Based on Regular Subgroups of the General Affine Group Probl. Inf. Transm. (IF 1.34) Pub Date : 20220410
I. Yu. MogilnykhA code is said to be propelinear if its automorphism group contains a subgroup acting on its codewords regularly. A subgroup of the group \(GA(r,q)\) of affine transformations is said to be regular if it acts regularly on vectors of \(\mathbb{F}_q^r\). Every automorphism of a regular subgroup of the general affine group \(GA(r,q)\) induces a permutation on the cosets of the Hamming code of length

Weakly Resolvable Block Designs and Nonbinary Codes Meeting the Johnson Bound Probl. Inf. Transm. (IF 1.34) Pub Date : 20220410
L. A. Bassalygo, V. A. Zinoviev, V. S. LebedevWe present two new families of resolvable block designs. We introduce the notion of a weakly resolvable block design and prove the equivalence of such designs and nonbinary codes meeting the Johnson bound. We construct a new family of such codes.

Multitwisted Additive Codes with Complementary Duals over Finite Fields Probl. Inf. Transm. (IF 1.34) Pub Date : 20220410
S. Sharma, A. SharmaMultitwisted (MT) additive codes over finite fields form an important class of additive codes and are generalizations of constacyclic additive codes. In this paper, we study a special class of MT additive codes over finite fields, namely complementarydual MT additive codes (or MT additive codes with complementary duals) by placing ordinary, Hermitian, and \(\ast\) trace bilinear forms. We also derive

Reduction of Recursive Filters to Representations by Sparse Matrices Probl. Inf. Transm. (IF 1.34) Pub Date : 20220410
A. Yu. Barinov 
New Modularity Bounds for Graphs $$G(n,r,s)$$ and $$G_p(n,r,s)$$ Probl. Inf. Transm. (IF 1.34) Pub Date : 20220114
Derevyanko, N. M., Koshelev, M. M.We analyze the behavior of the modularity of \(G(n,r,s)\) graphs in the case of \(r=o(\sqrt{{n}})\) and \(n\to\infty\) and also that of \(G_p(n,r,s)\) graphs for fixed \(r\) and \(s\) as \(n\to\infty\). For \(G(n,r,s)\) graphs with \(r\ge cs^2\), we obtain substantial improvements of previously known upper bounds. Upper and lower bounds previously obtained for \(G(n,r,s)\) graphs are extended to the

On List Decoding of Certain $$\mathbb{F}_q$$ Linear Codes Probl. Inf. Transm. (IF 1.34) Pub Date : 20220114
Polyanskii, N. A.We present a list decoding algorithm for \(\mathbb{F}_q\)linear codes that generalize the Reed–Solomon \(s\)codes.

On Intersections of Reed–Muller Like Codes Probl. Inf. Transm. (IF 1.34) Pub Date : 20220114
Solov’eva, F. I.A binary code that has the parameters and possesses the main properties of the classical \(r\)thorder Reed–Muller code \(RM_{r,m}\) will be called an \(r\)thorder Reed–Muller like code and will be denoted by \(LRM_{r,m}\). The class of such codes contains the family of codes obtained by the Pulatov construction and also classical linear and \(\mathbb{Z}_4\)linear Reed–Muller codes. We analyze the

New Lower Bounds on the Fraction of Correctable Errors under List Decoding in Combinatorial Binary Communication Channels Probl. Inf. Transm. (IF 1.34) Pub Date : 20220114
A. G. D’yachkov, D. Yu. GoshkoderThe aim of the paper is to revive and develop results of an unpublished manuscript of A.G. D'yachkov. We consider a discrete memoryless channel (DMC) and prove a theorem on the exponential expurgation bound for list decoding with fixed list size \(L\). This result is an extension of the classical exponential error probability bound for optimal codes over a DMC to the list decoding model over a DMC

On Data Compression and Recovery for Sequences Using Constraints on the Spectrum Range Probl. Inf. Transm. (IF 1.34) Pub Date : 20220114
N. G. DokuchaevWe investigate the possibility of data recovery for finite sequences with constraints on their spectrum defined by a special discretization of the spectrum range. These sequences are dense in the space of all sequences. We show that uniqueness sets for them can be singletons.

On the Maximum $$f$$ Divergence of Probability Distributions Given the Value of Their Coupling Probl. Inf. Transm. (IF 1.34) Pub Date : 20220114
V. V. PrelovThe paper is a supplement to the author’s paper [1]. Here we present explicit upper bounds (which are optimal in some cases) on the maximum value of the \(f\)divergence \(D_f(P\,\\, Q)\) of discrete probability distributions \(P\) and \(Q\) provided that the distribution \(Q\) (or its minimal component \(q_{\min}\)) and the value of the coupling of \(P\) and \(Q\) are fixed. We also obtain an explicit

New Turán Type Bounds for Johnson Graphs Probl. Inf. Transm. (IF 1.34) Pub Date : 20220114
N. A. DubininWe obtain a new bound on the number of edges in induced subgraphs of Johnson graphs.

On the Generalized Concatenated Construction for the Nordstrom–Robinson Code and the Binary Golay Code Probl. Inf. Transm. (IF 1.34) Pub Date : 20220114
V.A. Zinoviev, D.V. ZinovievWe show that the Nordstrom–Robinson code and the extended binary Golay code are generalized concatenated codes of order 3.

On an Evaluation Method for Zeta Constants Based on a Number Theoretic Approach Probl. Inf. Transm. (IF 1.34) Pub Date : 20211007
Karatsuba, E. A.New formulas for zeta constants are obtained based on a number theoretic approach that is used in proving irrationality of some classical constants. Using these formulas, one can approximate zeta constants and their combinations by rational fractions and construct a new efficient evaluation method for them.

On Perfect and Reed–Muller Codes over Finite Fields Probl. Inf. Transm. (IF 1.34) Pub Date : 20211007
Romanov, A. M.We consider errorcorrecting codes over a finite field with \(q\) elements (\(q\)ary codes). We study relations between singleerrorcorrecting \(q\)ary perfect codes and \(q\)ary Reed–Muller codes. For \(q\ge 3\) we find parameters of affine Reed–Muller codes of order \((q1)m2\). We show that affine Reed–Muller codes of order \((q1)m2\) are quasiperfect codes. We propose a construction which

Geometric Interpretation of Entropy: New Results Probl. Inf. Transm. (IF 1.34) Pub Date : 20211007
Dvorkin, G. D.We consider a relation between the metric entropy and local boundary deformation rate (LBDR) in the symbolic case. We prove that the LBDR understood as a limit in the mean is equal to the entropy for systems containing an essentially synchronized subshift of full measure. We also obtain an example of this relation in the case where such a subshift is lacking. We show for the first time that if the

Feedback InsertionDeletion Codes Probl. Inf. Transm. (IF 1.34) Pub Date : 20211007
Maringer, G., Polyanskii, N. A., Vorobyev, I. V., Welter, L.A new problem of transmitting information over the adversarial insertiondeletion channel with feedback is introduced. Assume that the encoder transmits \(n\) binary symbols one by one over a channel in which some symbols can be deleted and some additional symbols can be inserted. After each transmission, the encoder is notified about insertions or deletions that have occurred within the previous transmission

Analysis of Properties of Dyadic Patterns for the Fast Hough Transform Probl. Inf. Transm. (IF 1.34) Pub Date : 20211007
Karpenko, S. M., Ershov, E. I.We obtain an estimate for the maximum deviation from a geometric straight line to a discrete (dyadic) pattern approximating this line which is used for computing the fast Hough transform (discrete Radon transform) for a square image with side \(n=2^p\), \(p\in\mathbb{N}\). For \(p\) even, the maximum deviation amounts to \({p}/{6}\). An important role in the proof is played by analysis of subtle properties

Bounds on the Cardinality of Subspace Codes with Nonmaximum Code Distance Probl. Inf. Transm. (IF 1.34) Pub Date : 20211007
Gabidulin, E. M., Pilipchuk, N. I., Trushina, O. V.We study subspace codes with nonmaximum code distance. As opposed to spreads, i.e., codes with the maximum subspace distance, we refer to them as nonspreads here. We consider families of nonspreads based on using the Silva–Kötter–Kschischang (SKK) subspace code construction and Gabidulin–Bossert multicomponent codes with zero prefix (MZP). We give estimates for cardinalities of nonspreads for a large

On Minimax Detection of Gaussian Stochastic Sequences and Gaussian Stationary Signals Probl. Inf. Transm. (IF 1.34) Pub Date : 20211007
Burnashev, M. V.We consider the detection problem for Gaussian stochastic sequences (signals) with unknown covariance matrices in white Gaussian noise. For a given false alarm probability (1stkind error probability), the quality of minimax detection is given by the best miss probability (2ndkind error probability) exponent over a growing observation interval. The goal is finding the largest set of covariance matrices

Counting the Number of Perfect Matchings, and Generalized Decision Trees Probl. Inf. Transm. (IF 1.34) Pub Date : 20210707
M. N. VyalyiWe consider a generalization of the Pólya–Kasteleyn approach to counting the number of perfect matchings in a graph based on computing the symbolic Pfaffian of a directed adjacency matrix of the graph. Complexity of algorithms based on this approach is related to the complexity of the sign function of a perfect matching in generalized decision tree models. We obtain lower bounds on the complexity of

Separable CollusionSecure Multimedia Codes Probl. Inf. Transm. (IF 1.34) Pub Date : 20210707
E. E. Egorova, G. A. KabatianskyWe review known results about codes that are able to protect multimedia content from illegal redistribution by coalitions of malicious users.

Limit Theorems for the Maximal Path Weight in a Directed Graph on the Line with Random Weights of Edges Probl. Inf. Transm. (IF 1.34) Pub Date : 20210707
T. Konstantopoulos, A. V. Logachov, A. A. Mogulskii, S. G. FossWe consider an infinite directed graph with vertices numbered by integers \(\ldots,2, 1,0,1,2,\ldots\strut\), where any pair of vertices \(j< k\) is connected by an edge \((j,k)\) that is directed from \(j\) to \(k\) and has a random weight \(v_{j,k}\in [\infty,\infty)\). Here, \(\{v_{j,k},\: j< k\}\) is a family of independent and identically distributed random variables that take either finite

Minimax Theorems for Finite Blocklength Lossy Joint SourceChannel Coding over an Arbitrarily Varying Channel Probl. Inf. Transm. (IF 1.34) Pub Date : 20210707
A. S. Vora, A. A. KulkarniMotivated by applications in the security of cyberphysical systems, we pose the finite blocklength communication problem in the presence of a jammer as a zerosum game between the encoderdecoder team and the jammer, by allowing the communicating team as well as the jammer only locally randomized strategies. The communicating team's problem is nonconvex under locally randomized codes, and hence, in

Coding in a ZChannel in Case of Many Errors Probl. Inf. Transm. (IF 1.34) Pub Date : 20210707
V. S. Lebedev, N. A. PolyanskiiWe prove that the maximum number of words in a code that corrects a fraction of \(1/4+\varepsilon\) of asymmetric errors in a Zchannel is \(\Theta(\varepsilon^{3/2})\) as \(\varepsilon\to 0\).

Bounds on Borsuk Numbers in Distance Graphs of a Special Type Probl. Inf. Transm. (IF 1.34) Pub Date : 20210707
A. V. Berdnikov, A.M. RaigorodskiiIn 1933, Borsuk stated a conjecture, which has become classical, that the minimum number of parts of smaller diameter into which an arbitrary set of diameter 1 in \(\mathbb{R}^n\) can be partitioned is \(n+1\). In 1993, this conjecture was disproved using sets of points with coordinates 0 and 1. Later, the second author obtained stronger counterexamples based on families of points with coordinates

The f Divergence and Coupling of Probability Distributions Probl. Inf. Transm. (IF 1.34) Pub Date : 20210403
V. V. PrelovWe consider the problem of finding the minimum and maximum values of fdivergence for discrete probability distributions P and Q provided that one of these distributions and the value of their coupling are given. An explicit formula for the minimum value of the fdivergence under the above conditions is obtained, as well as a precise expression for its maximum value. This precise expression is not

Affine Variety Codes over a Hyperelliptic Curve Probl. Inf. Transm. (IF 1.34) Pub Date : 20210403
N. Patanker, S. K. SinghWe estimate the minimum distance of primary monomial affine variety codes defined from a hyperelliptic curve \({x^5} + x  {y^2}\) over \(\mathbb{F}_7\). To estimate the minimum distance of the codes, we apply symbolic computations implementing the techniques suggested by Geil and Özbudak. For some of these codes, we also obtain the symbolpair distance. Furthermore, lower bounds on the generalized

Finite Blocklength Analysis of Energy Harvesting Channels Probl. Inf. Transm. (IF 1.34) Pub Date : 20210403
K. G. Shenoy, V. SharmaWe consider additive white Gaussian noise channels and discrete memoryless channels where the transmitter harvests energy from the environment. These can model wireless sensor networks as well as Internet of Things. By providing a unifying framework that works for any energy harvesting channel, we study these channels assuming an infinite energy buffer and provide the corresponding achievability and

Tradeoff for Heterogeneous Distributed Storage Systems between Storage and Repair Cost Probl. Inf. Transm. (IF 1.34) Pub Date : 20210403
K. G. Benerjee, M. K. GuptaWe consider heterogeneous distributed storage systems (DSSs) having flexible reconstruction degree, where each node in the system has nonuniform repair bandwidth and nonuniform storage capacity. In particular, a data collector can reconstruct the file using some \(k\) nodes in the system and, for a node failure, the system can be repaired by some set of active nodes. Using mincut bound, we investigate

On the Generalized Concatenated Construction for Codes in $${L_1}$$ and Lee Metrics Probl. Inf. Transm. (IF 1.34) Pub Date : 20210403
V. A. Zinoviev, D. V. ZinovievWe consider a generalized concatenated construction for errorcorrecting codes over the qary alphabet in the modulus metric L1 and Lee metric L. Resulting codes have arbitrary length, arbitrary distance (independently of the alphabet size), and can correct both independent errors and error bursts in both metrics. In particular, for any length 2m we construct codes over \(\mathbb{Z}_4\) with Lee distance

Retraction Note: Note on “Smaller Explicit Superconcentrators” by N. Alon and M. Capalbo Probl. Inf. Transm. (IF 1.34) Pub Date : 20210127
L. A. BassalygoThis article has been retracted. Please see the Retraction Notice for more detail: https://doi.org/10.1134/S0032946020040092.

Polynomial Asymptotically Optimal Coding of Underdetermined Bernoulli Sources of the General Form Probl. Inf. Transm. (IF 1.34) Pub Date : 20210127
L. A. SholomovAn underdetermined Bernoulli source generates symbols of a given underdetermined alphabet independently with some probabilities. To each underdetermined symbol there corresponds a set of basic (fully defined) symbols such that it can be substituted (specified) by any of them. An underdetermined source is characterized by its entropy, which is implicitly introduced as a minimum of a certain function

Detecting Cycles of Length 10 in the Tanner Graph of a QCLDPC Code Based on Protograph Analysis Probl. Inf. Transm. (IF 1.34) Pub Date : 20210127
A. V. Kharin, K. N. Zavertkin, A. A. OvinnikovWe complete the description of the procedure of topological expansion of a bipartite graph without parallel branches on the plane of changing the structure of cycles of length up to 10 inclusive. Based on previous papers, we have extended a set of theorems specifying transformation rules for cycles and paths when passing from a protograph to the Tanner graph. We propose a procedure for detecting the

Existence and Construction of Complete Traceability Multimedia Fingerprinting Codes Resistant to Averaging Attack and Adversarial Noise Probl. Inf. Transm. (IF 1.34) Pub Date : 20210127
E. E. Egorova, M. Fernandez, G. A. Kabatiansky, Y. MiaoIt was shown very recently in [1] that there are no multimedia digital fingerprinting codes capable of fully recovering a coalition of malicious users under the general linear attack and adversarial noise. We show that such codes exist if the class of attacks is narrowed to the averaging attack. The arising mathematical problem is close to the problem of constructing signature codes for a noisy binary

A Sufficient Condition for the Existence of Restricted Fractional ( g , f )Factors in Graphs Probl. Inf. Transm. (IF 1.34) Pub Date : 20210127
S. Zhou, Z. Sun, Q. PanIn an NFV network, the availability of resource scheduling can be transformed to the existence of the fractional factor in the corresponding NFV network graph. Researching on the existence of special fractional factors in network structure can help to construct the NFV network with efficient application of resources. Let h: E(G) → [0, 1] be a function. We write \({d}_{G}^{h}(x)=\sum \limits_{e\ni x}h(e)\)

On Bases of BCH Codes with Designed Distance 3 and Their Extensions Probl. Inf. Transm. (IF 1.34) Pub Date : 20210127
I. Yu. Mogilnykh, F. I. Solov’evaWe consider narrowsense BCH codes of length pm − 1 over \({{\mathbb{F}}}_{p}\), m ≥ 3. We prove that neither such a code with designed distance δ = 3 nor its extension for p ≥ 5 is generated by the set of its codewords of the minimum nonzero weight. We establish that extended BCH codes with designed distance δ = 3 for p ≥ 3 are generated by the set of codewords of weight 5, where basis vectors can

On Stability of the Independence Number of a Certain Distance Graph Probl. Inf. Transm. (IF 1.34) Pub Date : 20210127
P. A. Ogarok, A. M. RaigorodskiiWe study the asymptotic behavior of the independence number of a random subgraph of a certain (r, s)distance graph. We provide upper and lower bounds for the critical edge survival probability under which a phase transition occurs, i.e., large new independent sets appear in the subgraph, which did not exist in the original graph.

Signaling to Relativistic Observers: An Einstein–Shannon–Riemann Encounter Probl. Inf. Transm. (IF 1.34) Pub Date : 20210127
M. KovačevićA communication scenario is described involving a series of events triggered by a transmitter and observed by a receiver experiencing relativistic time dilation. The message selected by the transmitter is assumed to be encoded in the events’ timings and is required to be perfectly recovered by the receiver, regardless of the difference in clock rates in the two frames of reference. It is shown that

Peculiar Properties of the p Linear Decomposition of p Linear Functions in Terms of the ShiftComposition Operation Probl. Inf. Transm. (IF 1.34) Pub Date : 20210127
I. V. CherednikWe analyze the shiftcomposition operation on discrete functions which occurs under homomorphisms of finite shift registers. We prove that for a prime p, in the class of all functions that are linear in the extreme variables, the notions of reducibility and plinear reducibility coincide for plinear functions. Furthermore, we show that a linear function irreducible in the class of all linear functions

The Sphere Packing Bound for Memoryless Channels Probl. Inf. Transm. (IF 1.34) Pub Date : 20201019
B. NakiboğluSphere packing bounds (SPBs)—with prefactors that are polynomial in the block length—are derived for codes on two families of memoryless channels using Augustin’s method: (possibly nonstationary) memoryless channels with (possibly multiple) additive cost constraints and stationary memoryless channels with convex constraints on the composition (i.e., empirical distribution, type) of the input codewords

Symmetric Block Designs and Optimal Equidistant Codes Probl. Inf. Transm. (IF 1.34) Pub Date : 20201019
L. A. Bassalygo, V. A. Zinoviev, V. S. LebedevWe prove that any symmetric block design (v, k, λ) generates optimal ternary and quaternary constantweight equidistant codes, whose parameters n, N, w, d, q are uniquely determined by the parameters of the block design. For one rather special case, we construct symbolwise uniform equidistant codes of the minimum length.

On Geometric Goppa Codes from Elementary Abelian p Extensions of $${{\mathbb{F}}}_{{p}^{s}}(x)$$ F p s ( x ) Probl. Inf. Transm. (IF 1.34) Pub Date : 20201019
N. Patanker, S. K. SinghLet p be a prime number and s > 0 an integer. In this short note, we investigate onepoint geometric Goppa codes associated with an elementary abelian pextension of \({{\mathbb{F}}}_{{p}^{s}}(x)\). We determine their dimension and exact minimum distance in a few cases. These codes are a special case of weak Castle codes. We also list exact values of the second generalized Hamming weight of these codes

Research on Fractional Critical Covered Graphs Probl. Inf. Transm. (IF 1.34) Pub Date : 20201019
S. Wang, W. ZhangA graph G is called a fractional (g, f)covered graph if for any e ∈ E(G), G admits a fractional (g, f)factor covering e. A graph G is called a fractional (g, f, n)critical covered graph if for any S ⊆ V(G) with ∣S∣ = n, G − S is a fractional (g, f)covered graph. A fractional (g, f, n)critical covered graph is said to be a fractional (a, b, n)critical covered graph if g(x) = a and f(x) = b for

Gaussian TwoArmed Bandit: Limiting Description Probl. Inf. Transm. (IF 1.34) Pub Date : 20201019
A. V. KolnogorovFor a Gaussian twoarmed bandit, which arises when batch data processing is analyzed, the minimax risk limiting behavior is investigated as the control horizon N grows infinitely. The minimax risk is searched for as the Bayesian one computed with respect to the worstcase prior distribution. We show that the highest requirements are imposed on the control in the domain of "close” distributions where

On Adaptive Estimation of Linear Functionals from Observations against White Noise Probl. Inf. Transm. (IF 1.34) Pub Date : 20200714
G. K. GolubevWe consider the problem of adaptive estimation of a linear functional of an unknown multivariate vector from its observations against white Gaussian noise. As a family of estimators for the functional, we use those generated by projection estimators of the unknown vector, and the main problem is to select the best estimator in this family. The goal of the paper is to explain and mathematically justify

Comparison of Contraction Coefficients for f Divergences Probl. Inf. Transm. (IF 1.34) Pub Date : 20200714
A. Makur, L. ZhengContraction coefficients are distribution dependent constants that are used to sharpen standard data processing inequalities for fdivergences (or relative fentropies) and produce socalled “strong” data processing inequalities. For any bivariate joint distribution, i.e., any probability vector and stochastic matrix pair, it is known that contraction coefficients for fdivergences are upper bounded

New Upper Bounds in the Hypothesis Testing Problem with Information Constraints Probl. Inf. Transm. (IF 1.34) Pub Date : 20200714
M. V. BurnashevWe consider a hypothesis testing problem where a part of data cannot be observed. Our helper observes the missed data and can send us a limited amount of information about them. What kind of this limited information will allow us to make the best statistical inference? In particular, what is the minimum information sufficient to obtain the same results as if we directly observed all the data? We derive

Detecting Cycles of Length 8 in the Tanner Graph of a QCLDPC Code Based on Protograph Analysis Probl. Inf. Transm. (IF 1.34) Pub Date : 20200714
A. V. Kharin, K. N. Zavertkin, A. A. OvinnikovFor cycles of length 8 in a Tanner graph, we propose an identification procedure based on the analysis of paths in a protograph. We formulate and prove a number of theorems that introduce identification rules for cycles and restrict the number of subgraphs to be analyzed. To distinguish between them, we propose a number of parameters that uniquely determine the group of analyzed paths in the protograph

Steiner Triple Systems of Order 21 with a Transversal Subdesign TD(3, 6) Probl. Inf. Transm. (IF 1.34) Pub Date : 20200416
Y. Guan, M. J. Shi, D. S. KrotovA 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

Piecewise Polynomial Sequences over the Galois Ring Probl. Inf. Transm. (IF 1.34) Pub Date : 20200416
A. R. VasinWe 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.

On q ary Codes with Two Distances d and d + 1 Probl. Inf. Transm. (IF 1.34) Pub Date : 20200416
P. Boyvalenkov, K. Delchev, D. V. Zinoviev, V. A. ZinovievWe consider qary 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.

On Distance Distributions of Orthogonal Arrays Probl. Inf. Transm. (IF 1.34) Pub Date : 20200416
N. L. ManevOrthogonal 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