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

Authors:
V. A. Zinoviev;D. V. Zinoviev
Affiliations:
Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia;Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia
Venue:
Problems of Information Transmission
Year:
2007

Citing 8
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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 驴 v 驴 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 驴 m + 1.