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Existence of Sequences Satisfying Bilinear Type Recurrence Relations Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-12-23 A. A. Illarionov
We study sequences \(\left\{A_n\right\}_{n=-\infty}^{+\infty}\) of elements of an arbitrary field \(\mathbb{F}\) that satisfy decompositions of the form $$ \begin{aligned} A_{m+n} A_{m-n}&=a_1(m) b_1(n)+a_2(m) b_2(n),\\ A_{m+n+1} A_{m-n}&=\widetilde a_1(m) \widetilde b_1(n)+\widetilde a_2(m) \widetilde b_2(n), \end{aligned} $$ where \(a_1,a_2,b_1,b_2\colon \mathbb{Z}\to\mathbb{F}\). We prove some results
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Near-Ideal Predictors and Causal Filters for Discrete-Time Signals Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-12-23 N. G. Dokuchaev
The paper presents linear predictors and causal filters for discrete-time signals featuring some different kinds of spectrum degeneracy. These predictors and filters are based on approximation of ideal noncausal transfer functions by causal transfer functions represented by polynomials of the Z-transform of the unit step signal.
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Geometric Interpretation of the Entropy of Sofic Systems Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-12-23 G. D. Dvorkin
We consider a geometric approach to the notion of metric entropy. We justify the possibility of this approach for the class of Borel invariant ergodic probability measures on sofic systems, which is the first result of such generality for non-Markovian systems.
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Invariant Measures for Contact Processes with State-Dependent Birth and Death Rates Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-12-23 E. A. Zhizhina, S. A. Pirogov
We consider contact processes on locally compact separable metric spaces with birth and death rates that are heterogeneous in space. We formulate conditions on the rates that ensure the existence of invariant measures of contact processes. One of the crucial conditions is the so-called critical regime condition. To prove the existence of invariant measures, we use the approach proposed in our preceding
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Constructions and Invariants of Optimal Codes in the Lee Metric Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-12-23 I. Yu. Mogilnykh, F. I. Solov’eva
We propose concatenation and switching methods for the construction of single-error-correcting perfect and diameter codes in the Lee metric. We analyze ranks and kernels of diameter perfect codes obtained by the switching construction.
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Feasibility of Data Transmission under Attack: From Isolated Toughness Variant Perspective Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-12-23 W. Gao, H. M. Başkonuş, C. Cattani
The graph model is an appreciable tool for data transmission network, where the feasibility of data transmission in site attack circumstances can be described by fractional critical graphs, and the vulnerability of networks can be measured by isolation toughness variant. This paper considers both the stability of the network and the feasibility of data transmission when the sites are destroyed, and
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Testing the Satisfiability of Algebraic Formulas over the Field of Two Elements Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-08-28 M. N. Vyalyi
We construct a probabilistic polynomial algorithm for testing the satisfiability of algebraic formulas of depth 3 over the two-element field, with addition as the top operation in the formulas. An algorithm with the same characteristics exists for the problem of testing whether a polynomial given by formulas of this type is identically zero (PIT problem). However, these problems and algorithms for
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Overparameterized Maximum Likelihood Tests for Detection of Sparse Vectors Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-08-28 G. K. Golubev
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Design and Decoding of Polar Codes with Large Kernels: A Survey Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-08-28 P. V. Trifonov
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Codes for Exact Support Recovery of Sparse Vectors from Inaccurate Linear Measurements and Their Decoding Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-08-28 M. Fernandez, G. A. Kabatiansky, S. A. Kruglik, Y. Miao
We construct codes that allow to exactly recover the support of an unknown sparse vector with almost equal absolute values of all nonzero coordinates given results of linear measurements in the presence of noise with \(\ell_p\)-norm bounded from above. We propose a decoding algorithm with asymptotically minimum complexity.
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Series of Formulas for Bhattacharyya Parameters in the Theory of Polar Codes Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-08-28 S. G. Kolesnikov, V. M. Leontiev
Bhattacharyya parameters are used in the theory of polar codes to determine positions of frozen and information bits. These parameters characterize rate of polarization of channels \(W_N^{(i)}\), \(1\le i\le N\), which are constructed in a special way from the original channel \(W\), where \(N=2^n\) is the channel length, \(n=1,2,\ldots\strut\). In the case where \(W\) is a binary symmetric memoryless
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Batch Poissonian Arrival Models of Multiservice Network Traffic Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-08-28 B. Ya. Lichtzinder, A. Yu. Privalov, V. I. Moiseev
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Covering Codes for the Fixed Length Levenshtein Metric Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-07-01
Abstract A covering code, or a covering, is a set of codewords such that the union of balls centered at these codewords covers the entire space. As a rule, the problem consists in finding the minimum cardinality of a covering code. For the classical Hamming metric, the size of the smallest covering code of a fixed radius \(R\) is known up to a constant factor. A similar result has recently been obtained
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Nonoverlapping Convex Polytopes with Vertices in a Boolean Cube and Other Problems in Coding Theory Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-01-10 A. Janabekova, G. A. Kabatiansky, I. Kamel, T. F. Rabie
We establish relations between several problems that are quite far from each other at first glance and formulate a number of open problems.
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Correcting a Single Error in Feedback Channels Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-01-10 I. V. Vorobyev, C. Deppe, A. V. Lebedev, V. S. Lebedev
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On One Construction Method for Hadamard Matrices Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-01-10 M. Villanueva, V. A. Zinoviev, D. A. Zinoviev
Using a concatenated construction for \(q\)-ary codes, we construct codes over \(\mathbb{Z}_q\) in the Lee metrics which after a proper mapping to the binary alphabet (which in the case of \(\mathbb{Z}_4\) is the well-known Gray map) become binary Hadamard codes (in particular, Hadamard matrices). Our construction allows to increase the rank and the kernel dimension of the resulting Hadamard code.
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Coupling of Several Random Variables Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-01-10 V. V. Prelov
We consider the problem of finding conditions under which an \(\alpha\)-coupling is possible for several random variables \(X_1,X_2,\ldots,X_k\) with a finite or countably infinite range of values and with given probability distributions, i.e., the possibility of constructing a joint distribution of these random variables such that \(\Pr\{X_1=X_2=\ldots=X_k\}=\alpha\).
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Remarks on Reverse Pinsker Inequalities Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-01-10 X. Y. Gui, Y. C. Huang
In this note we propose a simplified approach to recent reverse Pinsker inequalities due to O. Binette. More precisely, we give direct proofs of optimal variational bounds on f-divergence with possible constraints on relative information extrema. Our arguments are closer in spirit to those of Sason and Verdú.
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On Codes with Distances $$d$$ and $$n$$ Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-01-10 P. Boyvalenkov, K. Delchev, V. A. Zinoviev, D. V. Zinoviev
We enumerate all \(q\)-ary additive (in particular, linear) block codes of length \(n\) and cardinality \(N\ge q^2\) with exactly two distances: \(d\) and \(n\). For arbitrary codes of length \(n\) with distances \(d\) and \(n\), we obtain upper bounds on the cardinality via linear programming and using relationships to 2-distance sets on a Euclidean sphere.
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Lower Bound on the Minimum Number of Edges in Subgraphs of Johnson Graphs Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-01-10 Ya. K. Shubin
We prove a new lower bound on the minimum number of edges in subgraphs of Johnson graphs in the general case.
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Some Classes of Balanced Functions over Finite Fields with a Small Value of the Linear Characteristic Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-01-10 O. V. Kamlovskii, K. N. Pankov
We present balanced functions over finite fields with a small value of the linear characteristic. Previously, linear characteristics of similar classes of functions were studied for the two-element field only.
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Predictors for High Frequency Signals Based on Rational Polynomial Approximation of Periodic Exponentials Probl. Inf. Transm. (IF 1.2) Pub Date : 2023-01-10 N. G. Dokuchaev
We present linear integral predictors for continuous-time high-frequency signals with a finite spectrum gap. The predictors are based on approximation of a complex-valued periodic exponential (complex sinusoid) by rational polynomials.
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On Weight Distributions for a Class of Codes with Parameters of Reed-Muller Codes Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-10-04 I. Yu. Mogilnykh, F. I. Solov’eva
We present a new construction method for a doubly exponential class of binary codes with the parameters of Reed–Muller codes. We investigate the weight spectrum and the distance-invariance property of the proposed codes. In the constructed class of codes with the parameters of Reed–Muller codes, we show the existence of codes with the same weight distribution as for a Reed–Muller code and of codes
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On One Extremal Problem for Mutual Information Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-10-04 V. V. Prelov
We address the problem of finding the maximum of the mutual information \(I(X;Y)\) of two finite-valued random variables \(X\) and \(Y\) given only the value of their coupling, i.e., the probability \(\Pr\{X=Y\}\). We obtain explicit lower and upper bounds on this maximum, which in some cases are optimal.
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On Minimax Detection of Gaussian Stochastic Sequences with Imprecisely Known Means and Covariance Matrices Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-10-04 M. V. Burnashev
We consider the problem of detecting (testing) Gaussian stochastic sequences (signals) with imprecisely known means and covariance matrices. An alternative is independent identically distributed zero-mean Gaussian random variables with unit variances. For a given false alarm (1st-kind error) probability, the quality of minimax detection is given by the best miss probability (2nd-kind error probability)
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On the Reliability Function for a BSC with Noiseless Feedback at Zero Rate Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-10-04 M. V. Burnashev
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Fast Evaluation Algorithms for Elementary Algebraic and Inverse Functions Using the FEE Method Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-10-04 E. A. Karatsuba
We construct new fast evaluation algorithms for elementary algebraic and inverse functions based on application of two methods: A.A. Karatsuba’s method of 1960 and the author’s FEE method of 1990. The computational complexity is close to the optimal. The algorithms admit partial parallelization.
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Partitions into Perfect Codes in the Hamming and Lee Metrics Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-10-04 F. I. Solov’eva
We propose new combinatorial constructions of partitions into perfect codes in both the Hamming and Lee metrics. Also, we present a new combinatorial construction method for diameter perfect codes in the Lee metric, which is further developed to a construction of partitions into such codes. For the Lee metric, we improve previously known lower bounds on the number of perfect and diameter perfect codes
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Improved Upper Bounds for the Rate of Separating and Completely Separating Codes Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-10-04 I. V. Vorob’ev, V. S. Lebedev
A binary code is said to be an \((s,\ell)\)-separating code if for any two disjoint sets of its codewords of cardinalities at most \(s\) and \(\ell\) respectively, there exists a coordinate in which all words of the first set have symbol 0 while all words of the second have 1. If, moreover, for any two sets there exists a second coordinate in which all words of the first set have 1 and all words of
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Geometric Interpretation of Entropy for Dyck Systems Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-07-11 G. D. Dvorkin
We 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.
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Large Deviation Principle for Terminating Multidimensional Compound Renewal Processes with Application to Polymer Pinning Models Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-07-11 A. V. Logachov, A. A. Mogulskii, E. I. Prokopenko
We 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.
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Entropy in Thermodynamics and in Information Theory Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-07-11 V. A. Zorich
We discuss the relation between the concepts of entropy in thermodynamics and in information theory.
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Theoretical and Experimental Upper and Lower Bounds on the Efficiency of Convolutional Codes in a Binary Symmetric Channel Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-07-11 A. A. Kurmukova, F. I. Ivanov, V. V. Zyablov
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Poissonian Two-Armed Bandit: A New Approach Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-07-11 A. V. Kolnogorov
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On the Maximum Number of Non-Confusable Strings Evolving under Short Tandem Duplications Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-07-11 M. Kovačević
The 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 tandem-duplication mutations of length \({\le\! 3}\). In other words, any two such strings are non-confusable in the sense that they cannot produce the same string
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On New Problems in Asymmetric Cryptography Based on Error-Resistant Coding Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-07-11 V. V. Zyablov, F. I. Ivanov, E. A. Krouk, V. R. Sidorenko
We consider the problem of constructing a cryptosystem with a public key based on error-resistant 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 post-quantum cryptography. The main drawback of a code-based cryptosystem is a great length of the public key. Most papers devoted to reducing the cryptosystem
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Bounds on Threshold Probabilities for Coloring Properties of Random Hypergraphs Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-04-10 A. S. Semenov, D. A. Shabanov
We study the threshold probability for the property of existence of a special-form \(r\)-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
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On q-ary Propelinear Perfect Codes Based on Regular Subgroups of the General Affine Group Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-04-10 I. Yu. Mogilnykh
A 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
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Weakly Resolvable Block Designs and Nonbinary Codes Meeting the Johnson Bound Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-04-10 L. A. Bassalygo, V. A. Zinoviev, V. S. Lebedev
We 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.
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Multi-twisted Additive Codes with Complementary Duals over Finite Fields Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-04-10 S. Sharma, A. Sharma
Multi-twisted (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 complementary-dual MT additive codes (or MT additive codes with complementary duals) by placing ordinary, Hermitian, and \(\ast\) trace bilinear forms. We also derive
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Reduction of Recursive Filters to Representations by Sparse Matrices Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-04-10 A. Yu. Barinov
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New Modularity Bounds for Graphs $$G(n,r,s)$$ and $$G_p(n,r,s)$$ Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-01-14 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
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On List Decoding of Certain $$\mathbb{F}_q$$ -Linear Codes Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-01-14 Polyanskii, N. A.
We present a list decoding algorithm for \(\mathbb{F}_q\)-linear codes that generalize the Reed–Solomon \(s\)-codes.
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On Intersections of Reed–Muller Like Codes Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-01-14 Solov’eva, F. I.
A binary code that has the parameters and possesses the main properties of the classical \(r\)th-order Reed–Muller code \(RM_{r,m}\) will be called an \(r\)th-order 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
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New Lower Bounds on the Fraction of Correctable Errors under List Decoding in Combinatorial Binary Communication Channels Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-01-14 A. G. D’yachkov, D. Yu. Goshkoder
The 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
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On Data Compression and Recovery for Sequences Using Constraints on the Spectrum Range Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-01-14 N. G. Dokuchaev
We 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.
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On the Maximum $$f$$ -Divergence of Probability Distributions Given the Value of Their Coupling Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-01-14 V. V. Prelov
The 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
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New Turán Type Bounds for Johnson Graphs Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-01-14 N. A. Dubinin
We obtain a new bound on the number of edges in induced subgraphs of Johnson graphs.
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On the Generalized Concatenated Construction for the Nordstrom–Robinson Code and the Binary Golay Code Probl. Inf. Transm. (IF 1.2) Pub Date : 2022-01-14 V.A. Zinoviev, D.V. Zinoviev
We show that the Nordstrom–Robinson code and the extended binary Golay code are generalized concatenated codes of order 3.
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On an Evaluation Method for Zeta Constants Based on a Number Theoretic Approach Probl. Inf. Transm. (IF 1.2) Pub Date : 2021-10-07 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.
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On Perfect and Reed–Muller Codes over Finite Fields Probl. Inf. Transm. (IF 1.2) Pub Date : 2021-10-07 Romanov, A. M.
We consider error-correcting codes over a finite field with \(q\) elements (\(q\)-ary codes). We study relations between single-error-correcting \(q\)-ary perfect codes and \(q\)-ary Reed–Muller codes. For \(q\ge 3\) we find parameters of affine Reed–Muller codes of order \((q-1)m-2\). We show that affine Reed–Muller codes of order \((q-1)m-2\) are quasi-perfect codes. We propose a construction which
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Geometric Interpretation of Entropy: New Results Probl. Inf. Transm. (IF 1.2) Pub Date : 2021-10-07 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
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Feedback Insertion-Deletion Codes Probl. Inf. Transm. (IF 1.2) Pub Date : 2021-10-07 Maringer, G., Polyanskii, N. A., Vorobyev, I. V., Welter, L.
A new problem of transmitting information over the adversarial insertion-deletion 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
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Analysis of Properties of Dyadic Patterns for the Fast Hough Transform Probl. Inf. Transm. (IF 1.2) Pub Date : 2021-10-07 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
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Bounds on the Cardinality of Subspace Codes with Non-maximum Code Distance Probl. Inf. Transm. (IF 1.2) Pub Date : 2021-10-07 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
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On Minimax Detection of Gaussian Stochastic Sequences and Gaussian Stationary Signals Probl. Inf. Transm. (IF 1.2) Pub Date : 2021-10-07 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 (1st-kind error probability), the quality of minimax detection is given by the best miss probability (2nd-kind error probability) exponent over a growing observation interval. The goal is finding the largest set of covariance matrices
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Counting the Number of Perfect Matchings, and Generalized Decision Trees Probl. Inf. Transm. (IF 1.2) Pub Date : 2021-07-07 M. N. Vyalyi
We 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
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Separable Collusion-Secure Multimedia Codes Probl. Inf. Transm. (IF 1.2) Pub Date : 2021-07-07 E. E. Egorova, G. A. Kabatiansky
We review known results about codes that are able to protect multimedia content from illegal redistribution by coalitions of malicious users.
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Limit Theorems for the Maximal Path Weight in a Directed Graph on the Line with Random Weights of Edges Probl. Inf. Transm. (IF 1.2) Pub Date : 2021-07-07 T. Konstantopoulos, A. V. Logachov, A. A. Mogulskii, S. G. Foss
We 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