A translation of Problemy Peredachi Informatsii

Volume 32, Number 3, July–September, 1996
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In Memory of Roland L'vovich Dobrushin
pp. 223–238


Separating Systems of Conjunctions
V. Yu. Solomennikov
pp. 239–252

Abstract—A new kind of separating system over an alphabet of size $q\gt2$ is considered, in which the distance between two vectors is defined as the number of positions where they are different and both nonzero. Lower and upper bounds on the cardinality of such systems are obtained for linear and nonlinear cases. Some regular classes of separating systems are constructed. The mentioned systems arose in connection with problems of algebraic diagnosis, but they are also of independent significance.


Doubly Even Self-Dual $[40,20,8]$ Codes with Automorphism of an Odd Order
V. Yorgov and N. Ziapkov
pp. 253–257

Abstract—It is known that only the prime numbers $19$, $7$, $5$, $3$, and $2$ can divide the order of the automorphism group of a doubly even self-dual $[40,20,8]$ code. All these codes with automorphisms of order $19$, $7$, or $5$ with twenty fixed points are already known. In the present paper, all doubly even self-dual $[40,20,8]$ codes with automorphisms of order $5$ are constructed. The number of these nonequivalent codes equals $45$.


On the Nonsystematic Perfect Binary Codes
S. V. Avgustinovich and F. I. Solov'eva
pp. 258–261

Abstract—The existence of nonsystematic perfect binary codes of length $n$ is proved for every $n=2^{k}-1$, $k\geq8$.


Confidence Intervals in Adaptive Nonparametric Estimation of Regression
P. B. Bobrov and E. I. Ostrovskii
pp. 262–269

Abstract—Confidence intervals for the asymptotically optimal adaptive nonparametric estimates of regression are constructed under the assumption that the errors of measurements satisfy the existence condition of the higher-order moments or the condition $$ \operatorname{\bf P}\bigl(|\xi_i|>u\bigr)\leq C_2\exp(-C_3u^q), \quad u>0,\quad q>0. $$


Application of the Kotel'nikov Theorem in the Problem of Differentiating Functions with Finite Spectrum on a Nonuniform Interpolation Grid
Yu. G. Bulychev and I. V. Burlai
pp. 270–280

Abstract—Using the Kotel'nikov theorem, we obtain formulas for the $L$-fold differentiation of messages with finite spectrum that are given by their samples on a nonuniform interpolation grid. We find upper bounds on the error of differentiation caused by the truncation of an information message in the spatial domain. We show the possibility of applying the results obtained to the differentiation of messages that are approximated by functions with finite spectrum up to a definite precision. We find corresponding estimates for the systematic and random differentiation errors.


Closed Queueing Network with a Multiline Transmission Channel
O. V. Ivnitskii
pp. 281–289

Abstract—A closed queueing network with $n$ demands is considered. The demands are transmitted from one node of the network to another over an $r$-line transmission channel, $1\le r\le n$. The transmission time of the demands in the channel and the service time at the network nodes are assumed to be exponentially distributed random variables. The stationary probability distribution of the network states is found, which has a rather simple analytical form.


On Some Applications of the Semantic Evaluation Method
V. A. Lyubetsky
pp. 290–302

Abstract—A computer-oriented system of the semantic evaluation of statements is suggested. Its properties are studied and the corresponding propositions are proved. In particular, the possibility of reconstructing an object from a proof of its existence is shown, and the possibility of transferring various properties from ordered fields to special ordered rings is demonstrated (among such properties are Hilbert and Artin theorems, including upper bounds in them).