PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 17, Number 2, April–June, 1981
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CONTENTS

Cyclic $(L,g)$-Codes
N. A. Shekhunova and E. T. Mironchikov
pp. 77–82

Abstract—The authors develop a new approach to the construction of cyclic codes that makes it possible to improve the estimates for the maximum code distance in a number of cases.

On $B$-Functions Encountered in Modular Codes
S. D. Berman and I. I. Grushko
pp. 82–88

Abstract—Assume that $f(x)$ is a function from $\operatorname{\mathit GF}(2^m)$ to $\operatorname{\mathit GF}(2)$. Function $f(x)$ is called a $B$-function if all its Fourier–Hadamard coefficients $\sum\limits_u(-1)^{ux+f(x)}$ are equal to $\pm2^{m/2}$. $B$-functions play an important part in coding theory, particularly in the creation of Kerdock and Hadamard codes. The problem of classifying $B$-functions of degree $3$ is considered.

Rank-$3$ Graphs, Block Designs, and Codes with Unequal Symbol Protection
V. D. Tonchev
pp. 89–93

Abstract—The article considers binary codes with a parity-check matrix of type $(A,I)$, where $A$ is the adjacency matrix of a rank-3 graph. It is shown that, when a certain type of block design is present in the graph, the symbols of the second half of a code word have a higher degree of protection than is guaranteed by the minimum code weight. A detailed investigation is made of codes based on triangular and lattice graphs.

On a Coding Model for a Multiple-Access Adder Channel
A. G. Dyachkov and V. V. Rykov
pp. 94–104

Abstract—Upper and lower bounds are obtained for the length of an optimal code with zero error probability being some coding model for a multiple-access adder channel.

Method of Decoding Direct Sums of Products of Codes and Its Applications
I. M. Boyarinov
pp. 104–113

Abstract—The article proposes a method of decoding direct sums of iterative and concatenated codes, and investigates various applications.

On Packing Density for Unit Spheres in Hamming Space
G. L. Katsman
pp. 114–117

Abstract—The author constructs two nonlinear codes of length $66$ and $143$ that have minimum distance $3$ and cardinality $24\cdot2^{55}$ and $144^2\cdot2^{121}$, respectively. These codes are used to improve the lower limit for the lower bound of the packing density of spheres of radius $1$ in Hamming space.

Analysis of Second-Order Properties of Bayesian Estimates of Signal Parameter in White Gaussian Noise
M. V. Burnashev
pp. 117–126

Abstract—The article investigates asymptotic expansions of Bayesian estimates, as well as their distribution functions and moments, in the problem of estimating an unknown parameter on the basis of observation of a diffusion process.

Search for a Moving Signal in a Multichannel System by the Method of Degenerate Sequential Analysis
A. F. Terpugov and Yu. M. Tonkonogov
pp. 126–130

Abstract—The authors determine the characteristics of a signal search algorithm in a multichannel system using degenerate sequential analysis, for the case of a signal that shifts among the channel and for two models of its motion.

Allowance for Packet Propagation Delay in Random Multiple Access Systems
B. S. Tsybakov, V. A. Mikhailov, and S. P. Fedortsev
pp. 131–134

Abstract—The article considers random multiple access in a broadcast channel with allowance for the propagation delay. Stack algorithm 1 is considered as the access method. The largest transmission rate for this algorithm is determined as a function of the propagation time.

Asymptotic Invariance of Probabilistic Characteristics of Structurally Complex Switching Systems with Losses
G. I. Falin
pp. 134–139

Abstract—For an extensive class of systems, including non-full-access arrangements, various types of communication networks, etc., the author establishes asymptotic invariance of probability characteristics such as the blocking probability, distribution of number of busy paths, etc., in the sense that the first term in the expansion of the characteristics in powers in the arriving load is independent of the distribution of the duration of servicing for fixed average values of the latter.

On the Behavior of Automata in Uniform Markov Media
A. N. Boiko and V. I. Mukhin
pp. 139–148

Abstract—The article investigates the behavior of automata in uniform Markov media. Examples of purposeful and asymptotically optimal automata in such media are given. A lower bound is established for the number of states of a deterministic automaton that is purposeful in such media. A method is proposed for synthesizing automata with specified properties in these media from automata that have analogous properties in stationary random media.

BRIEF COMMUNICATIONS
(available in Russian only)

Construction of a Linear Pair of Uniquely Decodable Codes for a Noiseless Two-User Channel
G. G. Khachatrian
pp. 98–101 (Russian issue)

Abstract—We propose a new method for the construction of a linear pair of uniquely decodable codes for a two-user binary adder channel. Parameters of the constructed codes are better than those of previously known codes to within length 10. This makes it possible to improve the lower bound for the admissible pair of rates.

Note on the Weight Distribution for Constacyclic Codes
S. M. Dodunekov and V. I. Yorgov
pp. 102–103 (Russian issue)

Abstract—We show that the weight enumerator of any constacyclic code can be computed using the weight enumerator of a longer constacyclic code. As a corollary, we describe all equidistant constacyclic codes and propose an upper bound on the number of nonzero weights of an irreducible constacyclic code.

Capacity of a Random-Phase Quantum Channel
S. E. Fedorov and A. N. Mart'yanov
pp. 103–106 (Russian issue)

Abstract—We consider the potential error-correction capability of quantum equidistant signals with random phase. We show that a random-phase quantum communication channel has infinite capacity in the case of unlimited bandwidth and no thermal noise.