On switching equivalence of n-ary quasigroups of order 4 and perfect binary codes

On switching equivalence of n-ary quasigroups of order 4 and perfect binary codes We prove that arbitrary n-ary quasigroups of order 4 can be transformed into each other by successive switchings of {a, b}-components. We prove that perfect (closely packed) binary codes with distance 3 whose rank (dimension of the linear span) is greater by 1 or 2 than the rank of a linear perfect code can be taken to each other by successive switchings of i-components. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

On switching equivalence of n-ary quasigroups of order 4 and perfect binary codes

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Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2010 by Pleiades Publishing, Ltd.
Subject
Engineering; Systems Theory, Control; Information Storage and Retrieval; Electrical Engineering; Communications Engineering, Networks
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946010030026
Publisher site
See Article on Publisher Site

Abstract

We prove that arbitrary n-ary quasigroups of order 4 can be transformed into each other by successive switchings of {a, b}-components. We prove that perfect (closely packed) binary codes with distance 3 whose rank (dimension of the linear span) is greater by 1 or 2 than the rank of a linear perfect code can be taken to each other by successive switchings of i-components.

Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 19, 2010

References

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