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

Steiner triple systems S(2 m − 1, 3, 2) of rank 2 m − m+ 1 over $$\mathbb{F}_2$$ Steiner systems S(2 m − 1, 3, 2) of rank 2 m − m+1 over the field $$\mathbb{F}_2$$ are considered. A new recursive method for constructing Steiner triple systems of an arbitrary rank is proposed. The number of all Steiner systems of rank 2 m − m+1 is obtained. Moreover, it is shown that all Steiner triple systems S(2 m − 1, 3, 2) of rank r ≤ 2 m − m+1 are derived, i.e., can be completed to Steiner quadruple systems S(2 m , 4, 3). It is also proved that all such Steiner triple systems are Hamming; i.e., any Steiner triple system S(2 m − 1, 3, 2) of rank r ≤ 2 m − m + 1 over the field $$\mathbb{F}_2$$ occurs as the set of words of weight 3 of a binary nonlinear perfect code of length 2 m −1. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

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

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Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2012 by Pleiades Publishing, Ltd.
Subject
Engineering; Information Storage and Retrieval; Systems Theory, Control; Electrical Engineering; Communications Engineering, Networks
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946012020020
Publisher site
See Article on Publisher Site

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