Classification of optimal (v, 4, 1) binary cyclically permutable constant-weight codes and cyclic 2-(v, 4, 1) designs with v ≤ 76

Classification of optimal (v, 4, 1) binary cyclically permutable constant-weight codes and cyclic... We classify up to isomorphism optimal (v, 4, 1) binary cyclically permutable constantweight (CPCW) codes with v ≤ 76 and cyclic 2-(73, 4, 1) and 2-(76, 4, 1) designs. There is a one-to-one correspondence between optimal (v, 4, 1) CPCW codes, optimal cyclic binary constant-weight codes with weight 4 and minimum distance 6, (v, 4; ⌎(v − 1)/12⌏) difference packings, and optimal (v, 4, 1) optical orthogonal codes. Therefore, the classification of CPCW codes holds for them too. Perfect (v, 4, 1) CPCWcodes are equivalent to (v, 4, 1) cyclic difference families, and thus (73, 4, 1) cyclic difference families are classified too. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Classification of optimal (v, 4, 1) binary cyclically permutable constant-weight codes and cyclic 2-(v, 4, 1) designs with v ≤ 76

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Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2011 by Pleiades Publishing, Ltd.
Subject
Engineering; Information Storage and Retrieval; Electrical Engineering; Systems Theory, Control; Communications Engineering, Networks
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946011030021
Publisher site
See Article on Publisher Site

Abstract

We classify up to isomorphism optimal (v, 4, 1) binary cyclically permutable constantweight (CPCW) codes with v ≤ 76 and cyclic 2-(73, 4, 1) and 2-(76, 4, 1) designs. There is a one-to-one correspondence between optimal (v, 4, 1) CPCW codes, optimal cyclic binary constant-weight codes with weight 4 and minimum distance 6, (v, 4; ⌎(v − 1)/12⌏) difference packings, and optimal (v, 4, 1) optical orthogonal codes. Therefore, the classification of CPCW codes holds for them too. Perfect (v, 4, 1) CPCWcodes are equivalent to (v, 4, 1) cyclic difference families, and thus (73, 4, 1) cyclic difference families are classified too.

Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 11, 2011

References

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