On the nonexistence of triple-error-correcting perfect binary linear codes with a crown poset structure

There exist Steiner triple systems of or

There exist Steiner triple systems of order 15 that do not occur in a perfect binary one-error-correcting code

✍ Patric R. J. Östergård; Olli Pottonen 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 74 KB 👁 1 views

## Abstract The codewords at distance three from a particular codeword of a perfect binary one‐error‐correcting code (of length 2^m^−1) form a Steiner triple system. It is a longstanding open problem whether every Steiner triple system of order 2^m^−1 occurs in a perfect code. It turns out that thi