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

Östergård Patric R. J. | Zendy; Pottonen Olli | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

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

Author(s) -

Östergård Patric R. J.,

Pottonen Olli

Publication year - 2007

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.20122

Subject(s) - steiner system , mathematics , combinatorics , counterexample , order (exchange) , binary number , code (set theory) , code word , discrete mathematics , arithmetic , algorithm , computer science , decoding methods , set (abstract data type) , finance , economics , programming language

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

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research