PROBLEMS OF INFORMATION TRANSMISSION

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).