A179183 The size of an optimal binary code of length n and edit distance 3.

1, 2, 2, 4, 7, 12, 19, 34

Offset: 2

Author

Yeow Meng Chee (ymchee(AT)ntu.edu.sg), Jul 01 2010

Keywords

• nonn
• more

Comments

The edit distance between two words u and v is defined to be the minimum number of deletions, insertions, or substitutions required to change u to v.

a(10) >= 58, a(11) >= 104, a(12) >= 179. See link for examples of codes attaining these bounds. - Pontus von Brömssen, Mar 12 2024

Examples

			For n = 5, one can choose at most a(5) = 4 codewords at edit distance at least 3 from each other. One choice of 4 such codewords is 00110, 01001, 10000, and 11111. - _Pontus von Brömssen_, Dec 05 2018
		

Links

• Sheridan Houghten, A Table of Bounds on Optimal Fixed-Length Binary Edit-Metric Codes.
• Pontus von Brömssen, Lower bounds for A179183.

Crossrefs

Cf. A230380, A230381.

Extensions

a(9), modified name and comment from Sheridan Houghten, Oct 18 2013

Offset corrected by Pontus von Brömssen, Dec 05 2018