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Problemy Peredachi Informatsii, 2007, Volume 43, Issue 2, Pages 65–73
(Mi ppi12)
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This article is cited in 1 scientific paper (total in 1 paper)
Coding Theory
Some High Rate Linear Codes over $GF(5)$ and $GF(7)$
R. N. Daskalov Technical University of Gabrovo
Abstract:
Let an $[n,k,d]_q$ code be a linear code of length $n$, dimension $k$, and with minimum
Hamming distance $d$ over $GF(q)$. 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.
Received: 21.12.2006
Citation:
R. N. Daskalov, “Some High Rate Linear Codes over $GF(5)$ and $GF(7)$”, Probl. Peredachi Inf., 43:2 (2007), 65–73; Problems Inform. Transmission, 43:2 (2007), 124–131
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https://www.mathnet.ru/eng/ppi12 https://www.mathnet.ru/eng/ppi/v43/i2/p65
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Abstract page: | 333 | Full-text PDF : | 125 | References: | 31 | First page: | 6 |
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