# On resolvability of Steiner systems S(v = 2 m , 4, 3) of rank r ≤ v − m + 1 over \$\$\mathbb{F}_2 \$\$

On resolvability of Steiner systems S(v = 2 m , 4, 3) of rank r ≤ v − m + 1 over... Two new constructions of Steiner quadruple systems S(v, 4, 3) are given. Both preserve resolvability of the original Steiner system and make it possible to control the rank of the resulting system. It is proved that any Steiner system S(v = 2 m , 4, 3) of rank r ≤ v − m + 1 over F2 is resolvable and that all systems of this rank can be constructed in this way. Thus, we find the number of all different Steiner systems of rank r = v − m + 1. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

# On resolvability of Steiner systems S(v = 2 m , 4, 3) of rank r ≤ v − m + 1 over \$\$\mathbb{F}_2 \$\$

, Volume 43 (1) – Apr 20, 2007
15 pages

/lp/springer_journal/on-resolvability-of-steiner-systems-s-v-2-m-4-3-of-rank-r-v-m-1-over-6xv0r3ur5H
Publisher
Springer Journals
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/S003294600701005X
Publisher site
See Article on Publisher Site

### Abstract

Two new constructions of Steiner quadruple systems S(v, 4, 3) are given. Both preserve resolvability of the original Steiner system and make it possible to control the rank of the resulting system. It is proved that any Steiner system S(v = 2 m , 4, 3) of rank r ≤ v − m + 1 over F2 is resolvable and that all systems of this rank can be constructed in this way. Thus, we find the number of all different Steiner systems of rank r = v − m + 1.

### Journal

Problems of Information TransmissionSpringer Journals

Published: Apr 20, 2007

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