|
|
A057591
|
|
Maximal size of binary code of length n that corrects 2 deletions.
|
|
2
|
|
|
1, 1, 2, 2, 2, 4, 5, 7, 11, 16, 24
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Comments from Pablo San Segundo, Dec 04 2015 (Start): The search for a maximal clique in the graph 2dc.2048 has now finished. The answer is 24 (which was already known to be a lower bound).
The total time was 16.4 days using a 20-core XEON with 128Gb. 18 cores out of the 20 were in fact used.
The solution was found by a strong heuristic algorithm during pre-processing (about 5s). The actual search time was used "only" to prove optimality. The actual maximum clique algorithm is our most recent variant based on infra-chromatic BBMCX, described here, but as yet unpublished: https://www.researchgate.net/profile/Pablo_San_Segundo
The project was carried out by Pablo San Segundo and Jorge Artieda, Polytechnic University of Madrid (UPM), Center of Automation and Robotics (CAR). Supported by National Grant DPI 2014-53525-C3-1-R (End)
|
|
LINKS
|
N. J. A. Sloane, On single-deletion-correcting codes, in Codes and Designs (Columbus, OH, 2000), 273-291, Ohio State Univ. Math. Res. Inst. Publ., 10, de Gruyter, Berlin, 2002.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nice,hard,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Guenter Stertenbrink (Sterten(AT)aol.com) found a(9) = 11 and a(10) >= 16, Apr 28 2001
James B. Shearer (jbs(AT)pkmfgvm4.vnet.ibm.com) proved that a(10) = 16, Sep 20 2003
Pablo San Segundo and Jorge Artieda showed that a(11) = 24, Dec 04 2015
|
|
STATUS
|
approved
|
|
|
|