Volume 20, No 4, 2013, P. 46-64

UDC 621.391.15
Kovalevskaya D. I., Solov’eva F. I.
Steiner quadruple systems of small ranks and extended perfect binary codes

Abstract:
Using the switching method, we give a classification of Steiner quadruple systems of order $N>8$ and rank $r_N$ (different by 2 from the rank of the Hamming code of length $N$) which are embedded into extended perfect binary codes of length $N$ and the same rank. Lower and upper bounds for the number of such different systems are provided. The lower bound and description of different Steiner quadruple systems of order $N$ and rank $r_N$ which are not embedded into extended perfect binary codes of length $N$ and the same rank are given.
Tab. 4, bibliogr. 22.

Keywords: Steiner quadruple system, extended perfect binary code, switching, $il$- and $ijkl$-components, rank.

Kovalevskaya Darya Igorevna ¹
Solov’eva Faina Ivanovna ^1,2
1. S. L. Sobolev Institute of Mathematics, SB RAS,
4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
2. Novosibirsk State University,
2 Pirogov St., 630090 Novosibirsk, Russia
e-mail: daryik@rambler.ru, sol@math.nsc.ru