| n\d | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 1 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | 7 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 3 | 15 | 5 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 4 | 31 | 11 | 3 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 5 | 63 | 21 | 6 | 3 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 6 | 127 | 43 | 10 | 5 | 3 | 3 | 1 | 1 | 1 | 1 | 1 | 1 |
| 7 | 255 | 85 | 16 | 7 | 3 | 3 | 3 | 1 | 1 | 1 | 1 | 1 |
| 8 | 511 | 171 | 23-33 | 12 | 6 | 3 | 3 | 3 | 1 | 1 | 1 | 1 |
| 9 | 1023 | 341 | 40-67 | 16-25 | 7 | 5 | 3 | 3 | 3 | 1 | 1 | 1 |
| 10 | 2047 | 683 | 61-135 | 25-51 | 11 | 6 | 3 | 3 | 3 | 3 | 1 | 1 |
| 11 | 4095 | 1365 | 109-271 | 36-103 | 14-23 | 8 | 6 | 3 | 3 | 3 | 3 | 1 |
| 12 | 8191 | 2731 | 188-543 | 55-207 | 18-47 | 12-17 | 6 | 5 | 3 | 3 | 3-5 | 3 |
The above table shows E2(n,d), the number of codewords in an optimal binary code of minimum edit distance d, and for which n is the length of the longest codeword. Where exact values are not known, upper and lower bounds are provided.
The earliest version of this table appeared in: S.Baker, R.Flack and S.Houghten, "Optimal Variable-Length Insertion-Deletion Correcting Codes and Edit Metric Codes", Congressus Numerantium 186 (2008), 65-80.
If you have improvements, comments, etc, please e-mail houghten@brocku.ca
This page last modified 5th August 2008 © Copyright Sheridan Houghten, 2005-2008