PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Mutual and Coherent Information for Infinite-Dimensional Quantum Channels
A. S. Holevo and M. E. Shirokov
pp. 201–218

Abstract—The paper is devoted to the study of quantum mutual information and coherent information, two important characteristics of a quantum communication channel. Appropriate definitions of these quantities in the infinite-dimensional case are given, and their properties are studied in detail. Basic identities relating the quantum mutual information and coherent information of a pair of complementary channels are proved. An unexpected continuity property of the quantum mutual information and coherent information, following from the above identities, is observed. An upper bound for the coherent information is obtained.

On Switching Equivalence of $n$-ary Quasigroups of Order 4 and Perfect Binary Codes
D. S. Krotov and V. N. Potapov
pp. 219–224

Abstract—We prove that arbitrary $n$-ary quasigroups of order $4$ can be transformed into each other by successive switchings of $\{a,b\}$-components. We prove that perfect (closely packed) binary codes with distance $3$ whose rank (dimension of the linear span) is greater by $1$ or $2$ than the rank of a linear perfect code can be taken to each other by successive switchings of $i$-components.

Special Classes of Separable Goppa Codes with Improved Parameter Estimates
S. V. Bezzateev and N. A. Shekhunova
pp. 225–244

Abstract—We show that subclasses of $q$-ary separable Goppa codes $\Gamma(L,G)$ with $L=\{ \alpha\in \operatorname{\it GF}(q^{2\ell}):\: G(\alpha )\ne 0\}$ and with special Goppa polynomials $G(x)$ can be represented as a chain of equivalent and embedded codes. For all codes of the chain we obtain an improved bound for the dimension and find an exact value of the minimum distance. A chain of binary codes is considered as a particular case with specific properties.

A Class of Injective Compressing Maps on Linear Recurring Sequences over a Galois Ring
D. N. Bylkov
pp. 245–252

Abstract—We consider pseudorandom sequences $v$ over a field $\operatorname{\it GF}(p^r)$ obtained by mapping $\ell$-grams of a linear recurring sequence $u$ over a Galois ring to an arbitrary coordinate set. We study the possibility of uniquely reconstructing $u$ given $v$. Earlier known results are briefly overviewed.

Eigenspaces of the Discrete Walsh Transform
M. S. Bespalov
pp. 253–271

Abstract—We refine the notion of a discrete Walsh function and generalize the notion of a discrete Walsh transform, for which we propose a method for generating a corresponding $W$-matrix. We propose spectral decompositions of the discrete Walsh transform operators in arbitrary enumerations, as well as methods for finding bases of eigenspaces, one of them using a new direct product of matrices. We propose a notation for the fast discrete Walsh transform algorithm in the Paley enumeration. We construct Parseval frames for eigenspaces of the discrete Walsh transform in the Paley enumeration and demonstrate methods for applying them in error detection and correction.