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

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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 = 2m, 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.

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  1. Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia

    V. A. Zinoviev & D. V. Zinoviev

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  1. V. A. Zinoviev
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  2. D. V. Zinoviev
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Original Russian Text © V.A. Zinoviev, D.V. Zinoviev, 2007, published in Problemy Peredachi Informatsii, 2007, Vol. 43, No. 1, pp. 39–55.

Supported in part by the Russian Foundation for Basic Research, project no. 06-01-00226.

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Zinoviev, V.A., Zinoviev, D.V. On resolvability of Steiner systems S(v = 2m, 4, 3) of rank r ≤ v − m + 1 over \(\mathbb{F}_2 \) . Probl Inf Transm 43, 33–47 (2007). https://doi.org/10.1134/S003294600701005X

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