A transformation of Steiner quadruple systems S(υ, 4, 3) is introduced. For a given system, it allows to construct new systems of the same order, which can be nonisomorphic to the given one. The structure of Steiner systems S(υ, 4, 3) is considered. There are two different types of such systems, namely, induced and singular systems. Induced systems of 2-rank r can be constructed by the introduced transformation of Steiner systems of 2-rank r − 1 or less. A sufficient condition for a Steiner system S(υ, 4, 3) to be induced is obtained.
Problems of Information Transmission – Springer Journals
Published: Jan 21, 2010
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