Generalized Preparata codes and 2-resolvable Steiner quadruple systems

Generalized Preparata codes and 2-resolvable Steiner quadruple systems We consider generalized Preparata codes with a noncommutative group operation. These codes are shown to induce new partitions of Hamming codes into cosets of these Preparata codes. The constructed partitions induce 2-resolvable Steiner quadruple systems S(n, 4, 3) (i.e., systems S(n, 4, 3) that can be partitioned into disjoint Steiner systems S(n, 4, 2)). The obtained partitions of systems S(n, 4, 3) into systems S(n, 4, 2) are not equivalent to such partitions previously known. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Generalized Preparata codes and 2-resolvable Steiner quadruple systems

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Publisher
Pleiades Publishing
Copyright
Copyright © 2016 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/S0032946016020022
Publisher site
See Article on Publisher Site

Abstract

We consider generalized Preparata codes with a noncommutative group operation. These codes are shown to induce new partitions of Hamming codes into cosets of these Preparata codes. The constructed partitions induce 2-resolvable Steiner quadruple systems S(n, 4, 3) (i.e., systems S(n, 4, 3) that can be partitioned into disjoint Steiner systems S(n, 4, 2)). The obtained partitions of systems S(n, 4, 3) into systems S(n, 4, 2) are not equivalent to such partitions previously known.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jul 13, 2016

References

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