Abstract
AbstractThe codewords at distance three from a particular codeword of a perfect binary one‐error‐correcting code (of length 2m−1) form a Steiner triple system. It is a longstanding open problem whether every Steiner triple system of order 2m−1 occurs in a perfect code. It turns out that this is not the case; relying on a classification of the Steiner quadruple systems of order 16 it is shown that the unique anti‐Pasch Steiner triple system of order 15 provides a counterexample. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 465–468, 2007
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