Table 1 Addition and multiplication on GF(22)
From: Perfect Hamming code with a hash table for faster genome mapping
| + | 0 | 1 | α | α 2 | × | 0 | 1 | α | α 2 | |
| 0 | 0 | 1 | α | α 2 | 0 | 0 | 0 | 0 | 0 | |
| 1 | 1 | 0 | α 2 | α | 1 | 0 | 1 | α | α 2 | |
| α | α | α 2 | 0 | 1 | α | 0 | α | α 2 | 1 | |
| α 2 | α 2 | α | 1 | 0 | α 2 | 0 | α 2 | 1 | α |
From: Perfect Hamming code with a hash table for faster genome mapping
| + | 0 | 1 | α | α 2 | × | 0 | 1 | α | α 2 | |
| 0 | 0 | 1 | α | α 2 | 0 | 0 | 0 | 0 | 0 | |
| 1 | 1 | 0 | α 2 | α | 1 | 0 | 1 | α | α 2 | |
| α | α | α 2 | 0 | 1 | α | 0 | α | α 2 | 1 | |
| α 2 | α 2 | α | 1 | 0 | α 2 | 0 | α 2 | 1 | α |