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 |