16.4.2. КОД ГОЛЕЯ

Код Голея (23, 12, 7)
Marcel J.E. Golay


Способен исправлять тройные ошибки.

Порождающая матрица для кода Голея:

| 1 0 0 0 0 0 0 0 0 0 0   1 0 0 1 1 1 0 0 0 1 1 1 | 
| 0 1 0 0 0 0 0 0 0 0 0   1 0 1 0 1 1 0 1 1 0 0 1 |
| 0 0 1 0 0 0 0 0 0 0 0   1 0 1 1 0 1 1 0 1 0 1 0 |
| 0 0 0 1 0 0 0 0 0 0 0   1 0 1 1 1 0 1 1 0 1 0 0 |
| 0 0 0 0 1 0 0 0 0 0 0   1 1 0 0 1 1 1 0 1 1 0 0 |
| 0 0 0 0 0 1 0 0 0 0 0   1 1 0 1 0 1 1 1 0 0 0 1 |
| 0 0 0 0 0 0 1 0 0 0 0   1 1 0 1 1 0 0 1 1 0 1 0 |
| 0 0 0 0 0 0 0 1 0 0 0   1 1 1 0 0 1 0 1 0 1 1 0 |
| 0 0 0 0 0 0 0 0 1 0 0   1 1 1 0 1 0 1 0 0 0 1 1 |
| 0 0 0 0 0 0 0 0 0 1 0   1 1 1 0 0 0 0 0 1 1 0 1 |
| 0 0 0 0 0 0 0 0 0 0 1   0 1 1 1 1 1 1 1 1 1 1 1 |



Троичный код Голея

| 1 1 1 2 2 0 1 0 0 0 0 |
| 1 1 2 1 0 2 0 1 0 0 0 |
| 1 2 1 0 1 2 0 0 1 0 0 |
| 1 2 0 1 2 1 0 0 0 1 0 |
| 1 0 2 2 1 1 0 0 0 0 1 |