Binary extended perfect codes of length 16 and rank 14

Binary extended perfect codes of length 16 and rank 14 All extended binary perfect (16, 4, 211) codes of rank 14 over the field F 2 are classified. It is proved that among all nonequivalent extended binary perfect (16, 4, 211) codes there are exactly 1719 nonequivalent codes of rank 14 over F 2. Among these codes there are 844 codes classified by Phelps (Solov’eva-Phelps codes) and 875 other codes obtained by the construction of Etzion-Vardy and by a new general doubling construction, presented in the paper. Thus, the only open question in the classification of extended binary perfect (16,4,211) codes is that on such codes of rank 15 over F 2. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Binary extended perfect codes of length 16 and rank 14

Loading next page...
 
/lp/springer_journal/binary-extended-perfect-codes-of-length-16-and-rank-14-bAv2WgQ7YJ
Publisher
Nauka/Interperiodica
Copyright
Copyright © 2006 by Pleiades Publishing, Inc.
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946006020062
Publisher site
See Article on Publisher Site

Abstract

All extended binary perfect (16, 4, 211) codes of rank 14 over the field F 2 are classified. It is proved that among all nonequivalent extended binary perfect (16, 4, 211) codes there are exactly 1719 nonequivalent codes of rank 14 over F 2. Among these codes there are 844 codes classified by Phelps (Solov’eva-Phelps codes) and 875 other codes obtained by the construction of Etzion-Vardy and by a new general doubling construction, presented in the paper. Thus, the only open question in the classification of extended binary perfect (16,4,211) codes is that on such codes of rank 15 over F 2.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jul 7, 2006

References

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
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

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.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from
Google Scholar,
PubMed
Create lists to
organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off