A057657 Maximal size of binary code of length n that corrects one transposition (end-around transposition included).

2, 3, 4, 5, 8, 18, 28, 50, 100, 171, 316

Offset: 1

Author

N. J. A. Sloane, Oct 15 2000

Keywords

• nice
• hard
• nonn

References

• S. Butenko, P. Pardalos, I. Sergienko, V. P. Shylo and P. Stetsyuk, Estimating the size of correcting codes using extremal graph problems, Optimization, 227-243,
• Springer Optim. Appl., 32, Springer, New York, 2009.
• 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.

Links

• N. J. A. Sloane, Challenge Problems: Independent Sets in Graphs
• N. J. A. Sloane, On single-deletion-correcting codes

Crossrefs

Cf. A057608, A000016, A057591. Row sums of A085685.

Extensions

Typo in a(8) corrected and a(9) added, Jul 09 2003

a(9) = 100 from Butenko et al., Nov 28 2001 (see reference). Confirmed by N. J. A. Sloane, Jul 09 2003

a(10) >= 171 and a(100) >= 316 from Butenko et al., Nov 28 2001 (see reference).

a(10) = 171 from Brian Borchers (borchers(AT)nmt.edu), Apr 14 2005

a(11) = 316 from Brian Borchers (borchers(AT)nmt.edu), Nov 04 2009