Geodesic
Steiner quadruple systems of small ranks and extended perfect binary codes
Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 4, pp. 46-64.

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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. 
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D. I. Kovalevskaya; F. I. Solov'eva. Steiner quadruple systems of small ranks and extended perfect binary codes. Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 4, pp. 46-64. http://geodesic.mathdoc.fr/item/DA_2013_20_4_a4/

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