# Some high-rate linear codes over GF(5) and GF(7)

Some high-rate linear codes over GF(5) and GF(7) 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

# Some high-rate linear codes over GF(5) and GF(7)

, Volume 43 (2) – Jul 23, 2007
8 pages

/lp/springer_journal/some-high-rate-linear-codes-over-gf-5-and-gf-7-FFD0CLILd5
Publisher
Nauka/Interperiodica
Subject
Engineering; Communications Engineering, Networks; Electronic and Computer Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946007020056
Publisher site
See Article on Publisher Site

### 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.

### Journal

Problems of Information TransmissionSpringer Journals

Published: Jul 23, 2007

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 12 million articles from more than
10,000 peer-reviewed journals.

All for just \$49/month

### Stay up to date

It’s easy to organize your research with our built-in tools.

### Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

### DeepDyve Pro

Price
FREE
\$49/month

\$360/year
Save searches from Google Scholar, PubMed
Create lists to organize your research
Export lists, citations