9.12 The twenty binary dimension-six defects
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A lower-unitriangular binary matrix is encoded by reading the strict lower entries row by row:
\[
(1,0),
(2,0),(2,1),
\ldots,
(5,0),\ldots,(5,4).
\]
The resulting fifteen-bit integer is denoted by \(\operatorname{code}(A)\). A row is displayed as the integer whose binary expansion is its support vector. Table 9.5 lists all defects. Every row has \({\ell_{\downarrow}}=7\) and \({\ell_{*}}=6\).
| code | \(R_0\) | \(R_1\) | \(R_2\) | \(R_3\) | \(R_4\) | \(R_5\) |
|---|---|---|---|---|---|---|
| 6585 | 1 | 3 | 4 | 15 | 22 | 38 |
| 6641 | 1 | 3 | 4 | 14 | 23 | 38 |
| 6649 | 1 | 3 | 4 | 15 | 23 | 38 |
| 7601 | 1 | 3 | 4 | 14 | 22 | 39 |
| 7609 | 1 | 3 | 4 | 15 | 22 | 39 |
| 7665 | 1 | 3 | 4 | 14 | 23 | 39 |
| 10014 | 1 | 2 | 7 | 11 | 28 | 41 |
| 11038 | 1 | 2 | 7 | 11 | 28 | 42 |
| 12894 | 1 | 2 | 7 | 11 | 25 | 44 |
| 12958 | 1 | 2 | 7 | 11 | 26 | 44 |
| 13142 | 1 | 2 | 7 | 10 | 29 | 44 |
| 13198 | 1 | 2 | 7 | 9 | 30 | 44 |
| 14102 | 1 | 2 | 7 | 10 | 28 | 45 |
| 15118 | 1 | 2 | 7 | 9 | 28 | 46 |
| 17912 | 1 | 2 | 4 | 15 | 23 | 49 |
| 18936 | 1 | 2 | 4 | 15 | 23 | 50 |
| 19960 | 1 | 2 | 4 | 15 | 23 | 51 |
| 20984 | 1 | 2 | 4 | 15 | 23 | 52 |
| 22008 | 1 | 2 | 4 | 15 | 23 | 53 |
| 23032 | 1 | 2 | 4 | 15 | 23 | 54 |
For example, the canonical target has row encoding
\[
(1,3,4,14,23,39)
\]
and code \(7601\).