A010101 Maximal size of binary code of length n and asymmetric distance 2.

1, 2, 2, 4, 6, 12, 18, 36, 62

Offset

1,2

Comments

Size of optimal single-error-correcting code for Z-channel.

Next 3 terms are known to be in the range 112-117, 198-210 and 379-410 respectively.

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.

T. Etzion, New lower bounds for asymmetric and unidirectional codes, IEEE Trans. Inform. Theory, 37 (1991), 1696-1705.

J. H. Weber, Bounds and Constructions for Binary Block Codes Correcting Asymmetric or Unidirectional Errors, Ph. D. Thesis, Tech. Univ. Delft, 1989.

J. H. Weber, C. de Vroedt and D. E. Boekee, Bounds and constructions for binary codes of length less than 24 and asymmetric distance less than 6, IEEE Trans. Inform. Theory, 34 (1988), 1321-1332.

Links

Table of n, a(n) for n=1..9.

Tuvi Etzion and Patric R. J. Östergård, Greedy and heuristic algorithms for codes and colorings, IEEE Transactions on Information Theory, 44 (1998), 382-388, [Wayback Machine copy].

N. J. A. Sloane, Challenge Problems: Independent Sets in Graphs

Crossrefs

Sequence in context: A291365 A154779 A332983 * A274942 A028408 A226452

Adjacent sequences: A010098 A010099 A010100 * A010102 A010103 A010104

Keyword

nonn,nice,hard

Author

N. J. A. Sloane

Status

approved