PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Code Parameters of Principal Ideals of Group Algebra of Group $(2,2,\ldots,2)$ over Field of Characteristic $2$
S. D. Berman and I. I. Grushko
pp. 239–246

Abstract—Assume that $G$ is the direct product of $m$ groups of order $2$; $\pi$ is a field of two elements; and $\pi G$ is a group algebra of $G$ over $\pi$. Nonzero element $u\in\pi G$ is called nondecreasable if the code distance of the principal ideal $(u)$ is equal to the weight of element $u$. Necessary and sufficient nondecreasability conditions are derived for all elements of a second-order RM code and for those elements of a third-order RM code that are specified by a pair of quadratic forms over $\pi$. It is shown that those elements of an RM code of arbitrary order whose weight does not exceed twice the code distance of the smallest RM code containing the given element are nondecreasable.

Systematic Codes That Can Be Realized by Simple Circuits
N. D. Vvedenskaya and S. I. Gelfand
pp. 246–254

Abstract—Systematic binary linear codes with simple hardware implementation of coding are constructed.

Message-Source Models and Their Applications
N. N. Evtikhiev and E. A. Sandler
pp. 254–259

Abstract—The authors examine models of stationary discrete sources which constitute completely deterministic dynamic systems. It is shown that such models can be conveniently used for coding of sources by sliding blocks, which can yield, for stationary coder and decoder, maximum entropy of the code sequences. Aspects of the use of these models for noise-stable coding by sliding blocks are also considered. Fairly simple explicit models specified by means of piecewise-linear transformations of unit squares are constructed for Markov sources.

Free Synchronous Packet Access in a Broadcast Channel with Feedback
B. S. Tsybakov and V. A. Mikhailov
pp. 259–280

Abstract—New algorithms for random synchronous access of packets in a broadcast channel with feedback are posed. The transmission rate and delay for one of them are investigated. Unlike the familiar ALOHA system, the algorithm in question is stable and offers the possibility of transmission at rates greater than $1/e$ for finite delay.

On System of Flows in a Network
M. V. Lomonosov
pp. 280–290

Abstract—A new approach to the problem of creating a system of simultaneous flows with specified strengths (“multiproduct flows”) in a network is offered.

Algorithm-Theoretic Approach to Games
G. L. Kurdyumov
pp. 290–297

Abstract—A nontraditional approach to games based on the concepts of the theory of algorithms is proposed. A game is regarded as a process of interaction between ideal computers that additionally are furnished with random-signal generators. A universal language is proposed for describing game rules and strategies. Formal definitions of fundamental game concepts are given and a number of theorems are presented. As one possible application of the algorithm-theoretic investigation of games, the author suggests the creation of a universal game system, i.e., a computer program capable of playing any game. The prospects for practical utilization of systems of this type are also discussed.

On Number of Checks for Determining Significant Variables of Boolean Functions
I. I. Viktorova and A. M. Leontovich
pp. 298–306

Abstract—Assume that we have a Boolean function $\tilde{f}(x_0,\ldots, x_{n-1})$ which in reality depends only on $m$ variables: $\tilde{f}(x_0,\ldots, x_{n-1})\equiv f(x_{i_1}\ldots,x_{i_m})$. Function $f$ is known, but the numbers of the significant variables $i_1,\ldots,i_m$ are not. We wish to determine these numbers. In one check we can learn the value of $\tilde{f}(x_0,\ldots, x_{n-1})$ for an arbitrary combination of variables $x_0,\ldots, x_{n-1}$. The paper offers bounds for the number of checks over which the numbers $i_1,\ldots,i_m$ can be found with certainty, and also some specific algorithms for finding these numbers.

Double- and Triple-Defect-Correcting Codes
V. V. Losev, V. K. Konopel'ko, and Yu. D. Karyakin
pp. 307–310

Abstract—Codes for double and triple defect correction are described.

On Convergence of Delay Time Distribution in Two Problems of Sequential Analysis
M. Ya. Kelbert
pp. 310–312

Abstract—The “discrepancy” problem, namely that of most rapid detection of a violation of steady-state conditions, is considered here. It is shown that the mean and distribution of the delay time converge when a continuous scheme is approximated by discrete schemes. Similar results are obtained in the problem of successive discrimination of two simple hypotheses.

On Computations with Limited Storage of Entries
V. K. Bulitko and D. Probst
pp. 313–315

Abstract—Single-tape Turing machines that generate binary sequences are considered. It is not assumed that the entries in the cells of the tape can be stored permanently. The storage time for a symbol in a cell depends in some way on the number of cycles involved in generating and restoring it. A law is given that ensures that any computable sequence can be generated.

Completeness of Regular Codes
L. Staiger
pp. 316–317

Abstract—Five completeness conditions for regular codes are considered; it is shown that they are equivalent despite the fact that no two of them are equivalent for the case of arbitrary codes.

INDEX
pp. 319–324