✦ LIBER ✦
There exist Steiner triple systems of order 15 that do not occur in a perfect binary one-error-correcting code
✍ Scribed by Patric R. J. Östergård; Olli Pottonen
- Publisher
- John Wiley and Sons
- Year
- 2007
- Tongue
- English
- Weight
- 74 KB
- Volume
- 15
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
✦ Synopsis
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 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