PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Characterization of Two Classes of Codes that Attain the Griesmer Bound
S. M. Dodunekov and N. L. Manev
pp. 253–259

Abstract—Linear binary codes are considered. It is shown that, to within isomorphism, there exists a unique code with parameters $[2^k-2^{k-i}-3, k, 2^{k-1}-2^{k-i-1}-2]$, $2\leq i\leq k-4$, and two nonisomorphic codes with parameters $[2^k-11, k, 2^{k-1}-6], k\geq 5$.

Binary Self-Dual Codes with Automorphisms of Odd Order
V. I. Yorgov
pp. 260–270

Abstract—The article considers binary self-dual codes with an automorphism of odd prime order. New constraints are obtained for possible cyclical structures of the automorphism. The structure of the codes is investigated. All extremal even self-dual codes of length $40$, for which the order of the group of automorphisms can be divided by a prime $p\gt 5$, are obtained.

Hadamard-Type Block Designs and Self-Dual Codes
V. D. Tonchev
pp. 270–274

Abstract—The article considers binary self-dual doubly even $(16m+8,8m+4)$ codes with generating matrix that is specified by means of the incidence matrix of a Hadamard block design with parameters $2-(8m+3,4m+2,2m+1)$. It is shown that for $m\gt 0$ the minimum weight of the code is equal to at least $8$. Codes for $m\leq 2$ are extremal. It is shown that the six nonisomorphic $2-(19,10,5)$ block designs yield three nonequivalent extremal $(40, 20)$ codes.

Minimax Extrapolation of Sequences
G. K. Golubev and M. S. Pinsker
pp. 275–283

Abstract—The article considers optimal minimax extrapolation by $m$ steps for sequences that are the responses of a linear filter.

To the Theory of Discrete Signal Processing
S. D. Berman and I. I. Grushko
pp. 284–288

Abstract—Assume that $G$ is a finite group. A general definition of the $G$-spectrum of a discrete signal, that utilizes irreducible representations of group $G$, is given. If $G$ is an Abelian group, then the $G$-spectrum coincides with the familiar definition. The general definition of $G$-spectrum preserves all the advantages of spectral processing of discrete signals that are inherent in the Abelian case. For lengths that are powers of $2$, an infinite sequence $\{G_n\}$ of non-Abelian groups is constructed, for which the $G_n$-spectrum can be calculated $3/4$ times more rapidly than the FFT allows in the Abelian case for the same lengths.

Existence and Uniqueness Conditions for a Random Field Describing the State of a Switching Network
M. Ya. Kel'bert and Yu. M. Sukhov
pp. 289–304

Abstract—Sufficient existence and uniqueness conditions are given for the joint distribution of external and internal message flows on the lines of a switching network.

Random Multiple Access of “Impatient” Packets to a Broadcast Channel
B. S. Tsybakov and N. D. Vvedenskaya
pp. 305–313

Abstract—The authors consider the operation of a stack algorithm in a multiple-access system for the case in which packets that come into conflict leave the system, with some probability, without obtaining successful transmission.

Processes of Self-Assembly of Trees with Dependent Connections
M. L. Tai
pp. 313–319

Abstract—Results obtained earlier for processes of self-assembly of segments [A.M. Leontovich, Probl. Peredachi Inf., 1975, vol. 11, no. 4, pp. 97–105] are generalized to processes of self-assembly of trees with intensities of tree formation and breakage that depend on which trees are combined and which are obtained after breakage respectively. The system of differential equations satisfied by the connection concentrations is obtained. Processes of self-assembly of trees that break down into nests are introduced. An invariant state manifold is obtained in the phase space of a dynamic system that describes disintegrating processes of self-assembly of trees.

INDEX
pp. 321–326

Restricted Asynchronous Multiple Access
L. A. Bassalygo and M. S. Pinsker
pp. 92–96 (Russian issue)

Abstract—For a model of restricted multiple access without block synchronization, we estimate the minimum block length depending on the total number of nodes, number of messages from each node, and number of simultaneously operating nodes.

Universal Decoding for a Class of Deterministic Channels
A. V. Kuznetsov
pp. 97–100 (Russian issue)

Abstract—We derive upper and lower bounds on the maximum cardinality of a set of messages for which universal decoding is possible for an arbitrary class of deterministic channels that are assumed to be known while encoding.

On Derivation of Bispectra for Stationary Stochastic Process
V. A. Kalmykov
pp. 100–102 (Russian issue)

Abstract—Based on an artificially modeled realization of a random process $\xi_k$, $k=\pm 1,\dots\strut$, with a prescribed bispectral density $g(\lambda_1,\lambda_2)$, we construct and compare various estimates of the bispectral density. We show that using high-order weight functions in constructing an estimate for the bispectral density considerably reduces the estimation error.

Improvement of the Code-Length Lower Bound for a Multiple-Access Adder Channel
A. G. Dyachkov and V. V. Rykov
pp. 103–105 (Russian issue)

Abstract—In [1: A.G. D'yachkov and V.V. Rykov, Probl. Peredachi Inf., 1981, vol. 17, no. 2, pp. 26–38], the notion of a $B_s$-code was introduced for some coding problems for a multiple-access adder channel. These problems are related to conflict resolution in RMA systems [B.S. Tsybakov and V.A. Mikhailov, Probl. Peredachi Inf., 1978, vol. 14, no. 4, pp. 32–59; A.G. D'yachkov and V.V. Rykov, Proc. 6th All-Union Workshop on Comm. Networks, Part 4, Moscow, 1981, pp. 18–24]. In [1], upper and lower bounds for the length of optimum $B_s$-codes were obtained. In the present paper, we improve the lower bound from [1] for the case of odd $s$.