There Exist Steiner Triple Systems of Order 15 That Do Not Occur in a Perfect Binary One-Error-Correcting Code

Ostergard P.R.J. and Pottonen O. (2007) There Exist Steiner Triple Systems of Order 15 That Do Not Occur in a Perfect Binary One-Error-Correcting Code. Journal of Combinatorial Designs, 15 6: 465-468. doi:10.1002/jcd.20122


Author Ostergard P.R.J.
Pottonen O.
Title There Exist Steiner Triple Systems of Order 15 That Do Not Occur in a Perfect Binary One-Error-Correcting Code
Journal name Journal of Combinatorial Designs   Check publisher's open access policy
ISSN 1063-8539
Publication date 2007
Sub-type Article (original research)
DOI 10.1002/jcd.20122
Volume 15
Issue 6
Start page 465
End page 468
Total pages 4
Language eng
Subject 2607 Discrete Mathematics and Combinatorics
Abstract The 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.
Keyword Hamming code
Perfect code
Steiner quadruple system
Steiner triple system
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
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Citation counts: TR Web of Science Citation Count  Cited 4 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 5 times in Scopus Article | Citations
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