A057591 Maximal size of binary code of length n that corrects 2 deletions.

1, 1, 2, 2, 2, 4, 5, 7, 11, 16, 24

Offset: 1

Author

N. J. A. Sloane, Oct 05 2000

Keywords

• nice
• hard
• nonn

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actual maximum clique algorithm is our most recent variant based on infra-chromatic BBMCX, described here, but as yet unpublished: https://www.researchgate.net/profile/Pablo_San_Segundo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, Challenge Problems: Independent Sets in Graphs
• 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.
• N. J. A. Sloane, On single-deletion-correcting codes

Crossrefs

Cf. A000016, A057608, A057657, A010101.

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