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

%I #37 Mar 12 2024 15:49:59

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

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

%C 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.

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

%H Sheridan Houghten, <a href="http://www.cosc.brocku.ca/~houghten/binaryedit.html">A Table of Bounds on Optimal Fixed-Length Binary Edit-Metric Codes</a>.

%H Pontus von Brömssen, <a href="/A179183/a179183.txt">Lower bounds for A179183</a>.

%e 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

%Y Cf. A230380, A230381.

%K nonn,more

%O 2,2

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

%E a(9), modified name and comment from _Sheridan Houghten_, Oct 18 2013

%E Offset corrected by _Pontus von Brömssen_, Dec 05 2018