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

0,2

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

Table of n, a(n) for n=0..11.

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.

Sequence in context: A222126 A004045 A060200 * A060984 A226947 A272615

Adjacent sequences: A057605 A057606 A057607 * A057609 A057610 A057611

Keyword

nice,hard,nonn

Author

N. J. A. Sloane, Oct 09 2000

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

Status

approved