length n = 173
dimension k = 5
alphabet length q = 4
minimum distance d = 127
generator matrix:
| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 2 | 3 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 3 | 3 | 3 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 3 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 3 | 1 | 1 | 1 | 1 | 1 | 2 | 3 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 3 | 3 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 3 | 3 | 3 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 1 | 1 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 1 |
| 1 | 0 | 1 | 2 | 0 | 1 | 2 | 3 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 2 | 3 | 1 | 1 | 2 | 3 | 0 | 0 | 1 | 1 | 3 | 3 | 0 | 2 | 2 | 0 | 1 | 1 | 1 | 1 | 2 | 3 | 1 | 1 | 2 | 3 | 2 | 2 | 3 | 3 | 0 | 0 | 1 | 2 | 0 | 0 | 1 | 3 | 1 | 3 | 3 | 3 | 1 | 3 | 3 | 3 | 2 | 2 | 0 | 0 | 2 | 3 | 3 | 0 | 0 | 1 | 2 | 2 | 2 | 2 | 3 | 3 | 2 | 2 | 3 | 3 | 0 | 0 | 0 | 1 | 2 | 3 | 3 | 0 | 1 | 2 | 2 | 3 | 1 | 1 | 1 | 1 | 2 | 1 | 3 | 1 | 2 | 2 | 3 | 1 | 1 | 2 | 1 | 3 | 3 | 1 | 1 | 2 | 2 | 3 | 3 | 1 | 1 | 2 | 2 | 3 | 3 | 3 | 1 | 1 | 2 | 2 | 2 | 3 | 3 | 1 | 2 | 3 | 3 | 1 | 2 | 2 | 1 | 1 | 3 | 2 | 2 | 3 | 3 | 1 | 1 | 2 | 2 | 3 | 3 | 3 | 3 | 1 | 1 | 2 | 2 | 2 | 2 | 3 | 3 | 2 | 3 | 1 | 2 | 3 | 3 | 1 | 2 | 2 | 3 | 0 |
| 2 | 1 | 3 | 0 | 3 | 0 | 2 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 3 | 2 | 1 | 1 | 3 | 2 | 1 | 1 | 3 | 0 | 3 | 0 | 1 | 2 | 0 | 2 | 1 | 0 | 1 | 2 | 3 | 1 | 1 | 2 | 3 | 2 | 3 | 0 | 2 | 0 | 3 | 1 | 2 | 0 | 1 | 1 | 3 | 0 | 1 | 2 | 1 | 2 | 2 | 3 | 2 | 2 | 3 | 0 | 3 | 1 | 2 | 3 | 1 | 3 | 2 | 2 | 0 | 0 | 0 | 2 | 3 | 2 | 3 | 1 | 3 | 1 | 2 | 2 | 3 | 3 | 3 | 0 | 0 | 2 | 2 | 2 | 0 | 3 | 0 | 1 | 1 | 1 | 2 | 1 | 1 | 3 | 2 | 1 | 2 | 3 | 1 | 2 | 1 | 3 | 1 | 3 | 2 | 3 | 1 | 3 | 1 | 2 | 1 | 3 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 1 | 2 | 3 | 2 | 3 | 3 | 2 | 1 | 3 | 2 | 1 | 2 | 1 | 3 | 1 | 2 | 3 | 2 | 3 | 3 | 3 | 1 | 3 | 1 | 2 | 2 | 3 | 2 | 2 | 1 | 2 | 3 | 3 | 1 | 2 | 3 | 2 | 2 | 3 | 1 | 3 | 3 | 1 | 2 | 2 | 3 |
| 2 | 3 | 0 | 2 | 1 | 3 | 0 | 0 | 2 | 0 | 1 | 1 | 1 | 1 | 0 | 3 | 1 | 2 | 1 | 3 | 1 | 2 | 1 | 3 | 1 | 3 | 0 | 1 | 0 | 2 | 2 | 0 | 1 | 1 | 0 | 2 | 3 | 2 | 3 | 2 | 3 | 1 | 1 | 2 | 0 | 3 | 0 | 2 | 1 | 2 | 0 | 3 | 1 | 3 | 0 | 3 | 2 | 2 | 3 | 2 | 1 | 2 | 2 | 3 | 0 | 3 | 3 | 0 | 0 | 0 | 1 | 3 | 2 | 2 | 3 | 3 | 1 | 1 | 2 | 3 | 2 | 2 | 3 | 3 | 2 | 3 | 0 | 3 | 1 | 0 | 2 | 0 | 1 | 0 | 2 | 1 | 1 | 2 | 1 | 1 | 1 | 3 | 2 | 2 | 1 | 3 | 2 | 1 | 1 | 3 | 3 | 1 | 3 | 2 | 3 | 1 | 2 | 1 | 3 | 1 | 3 | 2 | 1 | 2 | 3 | 2 | 1 | 1 | 2 | 3 | 3 | 2 | 3 | 2 | 3 | 1 | 2 | 2 | 1 | 3 | 1 | 1 | 3 | 2 | 3 | 2 | 2 | 3 | 3 | 3 | 2 | 1 | 3 | 1 | 2 | 3 | 3 | 1 | 1 | 2 | 2 | 2 | 3 | 2 | 3 | 1 | 3 | 2 | 2 | 2 | 3 | 1 | 3 |
by adding the parity bit to 172