Abstract
Using the switching method, we give a classification for the Steiner quadruple systems of orderN > 8 and rank r N (different by 2 from the rank of the Hamming code of length N) which are embedded into the extended perfect binary codes of length N and the same rank. Some lower and upper bounds are provided on the number of these different systems. The lower bound and description of different Steiner quadruple systems of order N and rank r N which are not embedded into the extended perfect binary codes of length N and the same rank are given.
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