This article is cited in 1 paper

Coding Theory

Non-full-rank Steiner quadruple systems $S(v,4,3)$

V. A. Zinoviev, D. V. Zinoviev

Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

Abstract: All different Steiner systems $S(2^m,4,3)$ of order $2^m$ and rank $2^m-m-1+s$ over $\mathbb F_2$, where $0\le s\le m-1$, are constructed. The number of different systems $S(2^m,4,3)$ whose incident matrices are orthogonal to a fixed code is obtained. A connection between the number of different Steiner systems and of different Latin cubes is described.

UDC: 621.391.1+519.7

Received: 11.11.2013
Revised: 29.05.2014

 English version: Problems of Information Transmission, 2014, 50:3, 270–279

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