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

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• hard

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

• 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