The perfect binary one-error-correcting codes of length 15: Part II-properties

Ostergard, Patric R. J., Pottonen, Olli and Phelps, Kevin T. (2010) The perfect binary one-error-correcting codes of length 15: Part II-properties. IEEE Transactions on Information Theory, 56 6: 2571-2582. doi:10.1109/TIT.2010.2046197


Author Ostergard, Patric R. J.
Pottonen, Olli
Phelps, Kevin T.
Title The perfect binary one-error-correcting codes of length 15: Part II-properties
Journal name IEEE Transactions on Information Theory   Check publisher's open access policy
ISSN 0018-9448
1557-9654
Publication date 2010-01-01
Sub-type Article (original research)
DOI 10.1109/TIT.2010.2046197
Open Access Status Not Open Access
Volume 56
Issue 6
Start page 2571
End page 2582
Total pages 12
Place of publication Piscataway, NJ, United States
Publisher Institute of Electrical and Electronics Engineers
Language eng
Abstract A complete classification of the perfect binary one-error-correcting codes of length 15, as well as their extensions of length 16, was recently carried out in [P. R. J. Östergård and O. Pottonen, "The perfect binary one-error-correcting codes of length 15: Part I-Classification," IEEE Trans. Inf. Theory vol. 55, pp. 4657-4660, 2009]. In the current accompanying work, the classified codes are studied in great detail, and their main properties are tabulated. The results include the fact that 33 of the 80 Steiner triple systems of order 15 occur in such codes. Further understanding is gained on full-rank codes via switching, as it turns out that all but two full-rank codes can be obtained through a series of such transformations from the Hamming code. Other topics studied include (non)systematic codes, embedded one-error-correcting codes, and defining sets of codes. A classification of certain mixed perfect codes is also obtained.
Keyword Classification
Hamming code
Perfect code
Steiner system
Switching
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
 
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