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JOURNALS // Problemy Peredachi Informatsii // Archive

Probl. Peredachi Inf., 2009 Volume 45, Issue 4, Pages 26–42 (Mi ppi1997)

This article is cited in 6 papers

Coding Theory

On one transformation of Steiner quadruple systems $S(v,4,3)$

V. A. Zinoviev, D. V. Zinoviev

A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: A transformation of Steiner quadruple systems $S(v,4,3)$ 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 $S(v,4,3)$ 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 $S(v,4,3)$ to be induced is obtained.

UDC: 621.391.15+519.1

Received: 16.06.2008
Revised: 12.08.2009


 English version:
Problems of Information Transmission, 2009, 45:4, 317–332

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