DocumentCode :
1369888
Title :
The Perfect Binary One-Error-Correcting Codes of Length 
: Part I—Classification
Author :
Ostergard, P. ; Pottonen, O.
Author_Institution :
Dept. of Commun. & Networking, Helsinki Univ. of Technol. TKK, Helsinki, Finland
Volume :
55
Issue :
10
fYear :
2009
Firstpage :
4657
Lastpage :
4660
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.
Keywords :
Hamming codes; binary codes; error correction codes; Hamming code; Steiner quadruple systems; binary one-error-correcting codes; Automation; Binary codes; Electronic mail; Classification; Hamming code; Steiner system; perfect binary code;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.2009.2027525
Filename :
5238744
Link To Document :
