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

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