A translation of Problemy Peredachi Informatsii

Volume 43, Number 2, April–June, 2007
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Code Spectrum and the Reliability Function: Gaussian Channel
M. V. Burnashev
pp. 69–88

Abstract—A new approach to upper bounding the channel reliability function using the code spectrum is described. It allows us to treat both the low and high rate cases in a unified way. In particular, previously known upper bounds are improved and a new derivation of the sphere-packing bound is presented.


On Binary Self-complementary $[120,9,56]$ Codes Having an Automorphism of Order 3 and Associated SDP Designs
I. Bouyukliev, S. Bouyuklieva, and S. Dodunekov
pp. 89–96

Abstract—The number of known inequivalent binary self-complementary $[120,9,56]$ codes (and hence the number of known binary self-complementary $[136,9,64]$ codes) is increased from 25 to 4668 by showing that there are exactly 4650 such inequivalent codes with an automorphism of order 3. This implies that there are at least 4668 nonisomorphic quasi-symmetric SDP designs with parameters $(v=120,\, k=56,\, \lambda=55)$ and as many SDP designs with parameters $(v=136,\, k=64,\, \lambda=56)$.


On New Completely Regular $q$-ary Codes
V. A. Zinoviev and J. Rifà
pp. 97–112

Abstract—In this paper, new completely regular $q$-ary codes are constructed from $q$-ary perfect codes. In particular, several new ternary completely regular codes are obtained from the ternary $[11,6,5]$ Golay code. One of these codes with parameters $[11,5,6]$ has covering radius $\rho=5$ and intersection array $(22,20,18,2,1;1,2,9,20,22)$. This code is dual to the ternary perfect $[11,6,5]$ Golay code. Another $[10,5,5]$ code has covering radius $\rho=4$ and intersection array $(20,18,4,1;1,2,18,20)$. This code is obtained by deleting one position of the former code. All together, the ternary Golay code results in eight completely regular codes, only four of which were previously known. Also, new infinite families of completely regular codes are constructed from $q$-ary Hamming codes.


Uniqueness of Some Optimal Superimposed Codes
S. Hong, S. Kapralov, H. K. Kim, and D. Y. Oh
pp. 113–123

Abstract—Four new results on the uniqueness of optimal superimposed codes are presented, namely, the uniqueness of $(w,r)$ superimposed codes of size $N \times T$ with $N=\displaystyle\binom{w+r+1}{w}$ and $T=w+r+1$ and the uniqueness of $(2,2)$ superimposed codes of size $18 \times 9$, $(2,2)$ superimposed codes of size $14 \times 7$, and $(3,3)$ superimposed codes of size $66 \times 11$.


Some High-Rate Linear Codes over $\operatorname{\it GF}(5)$ and $\operatorname{\it GF}(7)$
R. Daskalov
pp. 124–131

Abstract—Let an $[n,k,d]_q$ code be a linear code of length $n$, dimension $k$, and with minimum Hamming distance $d$ over $\operatorname{\it GF}(q)$. The ratio $R=k/n$ is called the rate of a code. In this paper, $[62,53,6]_5$, $[62,48,8]_5$, $[71,56,8]_5$, $[124,113,6]_5$, $[43,36,6]_7$, $[33,23,7]_7$, and $[27,18,7]_7$ high-rate codes and new codes with parameters $[42,14,19]_5$, $[42,15,18]_5$, $[48,13,24]_5$, $[52,12,28]_5$, $[71,15,38]_5$, $[71,16,36]_5$, $[72,12,41]_5$, $[78,10,50]_5$, $[88,11,54]_5$, $[88,13,51]_5$, $[124,14,77]_5$, $[32,12,15]_7$, $[32,10,17]_7$, $[36,10,20]_7$, and $[48,10,29]_7$ are constructed. The codes with parameters $[62,53,6]_5$ and $[43,36,6]_7$ are optimal.


On Reconstruction of Information on an Input Word in a Medvedev Permutation Automaton Given Initial and Final States
A. V. Babash
pp. 132–142

Abstract—We give a description of Medvedev permutation automata for which approximate reconstruction of information on an input word is possible given initial and final states corresponding to the input word.


Playout in Slotted CBR Networks: Single and Multiple Nodes
A. Yu. Privalov and K. Sohraby
pp. 143–166

Abstract—We consider playout of a constant bit-rate (CBR) traffic after one or several multiplexors in a network with a playout buffer. Probabilistic characteristics of the playout process are found, depending on the traffic characteristics and parameters of the buffer. We present conditions on the buffer parameters that guarantee no jitter (complete playout).