A057608 Maximal size of binary code of length n that corrects one transposition (end-around transposition not included).

1, 2, 3, 4, 8, 12, 20, 38, 63, 110, 196, 352

Offset: 0

Author

N. J. A. Sloane, Oct 09 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

• José Manuel Gómez Soto, Jesús Leaños, Luis Manuel Ríos-Castro, Luis Manuel Rivera, On an error-correcting code problem, arXiv:1711.03682 [math.CO], 2017.
• N. J. A. Sloane, On single-deletion-correcting codes
• N. J. A. Sloane, Challenge Problems: Independent Sets in Graphs

Crossrefs

Cf. A057657, A000016, A057591, A010101. Row sums of A085684.

Extensions

a(9) = 110 from Butenko et al., Nov 28 2001 (see reference).

a(9) = 110 also from Ketan Narendra Patel (knpatel(AT)eecs.umich.edu), Apr 29 2002. Confirmed by N. J. A. Sloane, Jul 07 2003

a(10) >= 196 and a(11) >= 352 from Butenko et al., Nov 28 2001 (see reference).

a(10) = 196 found by N. J. A. Sloane, Jul 17 2003

a(11) = 352 proved by Brian Borchers (borchers(AT)nmt.edu), Oct 16 2009