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

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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

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