Structure of steiner triple systems S(2 m − 1, 3, 2) of rank 2 m − m + 2 over $\mathbb{F}_2 $

Structure of steiner triple systems S(2 m − 1, 3, 2) of rank 2 m − m + 2 over $\mathbb{F}_2 $ The structure of all different Steiner triple systems S(2 m −1, 3, 2) of rank 2 m −m+2 over $\mathbb{F}_2 $ is described. This induces a natural recurrent method for constructing Steiner triple systems of any rank. In particular, the method gives all different such systems of order 2 m − 1 and rank ≤ 2 m − m + 2. The number of such different systems of order 2 m − 1 and rank less than or equal to 2 m − m + 2 which are orthogonal to a given code is found. It is shown that all different triple Steiner systems of order 2 m − 1 and rank ≤ 2 m − m + 2 are derivative and Hamming. Furthermore, all such triples are embedded in quadruple systems of the same rank and in perfect binary nonlinear codes of the same rank. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Structure of steiner triple systems S(2 m − 1, 3, 2) of rank 2 m − m + 2 over $\mathbb{F}_2 $

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Publisher
Springer US
Copyright
Copyright © 2013 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/S0032946013030034
Publisher site
See Article on Publisher Site

Abstract

The structure of all different Steiner triple systems S(2 m −1, 3, 2) of rank 2 m −m+2 over $\mathbb{F}_2 $ is described. This induces a natural recurrent method for constructing Steiner triple systems of any rank. In particular, the method gives all different such systems of order 2 m − 1 and rank ≤ 2 m − m + 2. The number of such different systems of order 2 m − 1 and rank less than or equal to 2 m − m + 2 which are orthogonal to a given code is found. It is shown that all different triple Steiner systems of order 2 m − 1 and rank ≤ 2 m − m + 2 are derivative and Hamming. Furthermore, all such triples are embedded in quadruple systems of the same rank and in perfect binary nonlinear codes of the same rank.

Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 15, 2013

References

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