The perfect binary one-error-correcting codes of length 15. Part I: classification

Östergård, Patric R. J. and Pottonen, Olli (2009) The perfect binary one-error-correcting codes of length 15. Part I: classification. IEEE Transactions on Information Theory, 55 10: 4657-4660. doi:10.1109/TIT.2009.2027525


Author Östergård, Patric R. J.
Pottonen, Olli
Title The perfect binary one-error-correcting codes of length 15. Part I: classification
Journal name IEEE Transactions on Information Theory   Check publisher's open access policy
ISSN 0018-9448
1557-9654
Publication date 2009-10
Sub-type Article (original research)
DOI 10.1109/TIT.2009.2027525
Open Access Status
Volume 55
Issue 10
Start page 4657
End page 4660
Total pages 4
Place of publication Piscataway, NJ, United States
Publisher Institute of Electrical and Electronics Engineers
Language eng
Formatted abstract
A complete classification of the perfect binary one-error-correcting codes of length 15 as well as their extensions of length 16 is presented. There are 5983 such inequivalent perfect codes and 2165 extended perfect codes. Efficient generation of these codes relies on the recent classification of Steiner quadruple systems of order 16. Utilizing a result of Blackmore, the optimal binary one-error-correcting codes of length 14 and the (15, 1024, 4) codes are also classified; there are 38 408 and 5983 such codes, respectively.
Keyword Classification
Hamming code
perfect binary code
Steiner system
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
Versions
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 16 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 24 times in Scopus Article | Citations
Google Scholar Search Google Scholar
Created: Thu, 11 Sep 2014, 18:40:48 EST by Olli Pottonen on behalf of Mathematics