Table 3 A quasigroup \((Q,*)\) of order \(3^2\) and its representations based on GF(3)
From: An algorithm for judging and generating multivariate quadratic quasigroups over Galois fields
* | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
1 | 1 | 2 | 0 | 4 | 5 | 3 | 7 | 8 | 6 |
2 | 2 | 0 | 1 | 5 | 3 | 4 | 8 | 6 | 7 |
3 | 3 | 4 | 5 | 6 | 7 | 8 | 0 | 1 | 2 |
4 | 4 | 5 | 3 | 7 | 8 | 6 | 1 | 2 | 0 |
5 | 5 | 3 | 4 | 8 | 6 | 7 | 2 | 0 | 1 |
6 | 6 | 7 | 8 | 0 | 1 | 2 | 3 | 4 | 5 |
7 | 7 | 8 | 6 | 1 | 2 | 0 | 4 | 5 | 3 |
8 | 8 | 6 | 7 | 2 | 0 | 1 | 5 | 3 | 4 |
* | 00 | 01 | 02 | 10 | 11 | 12 | 20 | 21 | 22 |
|---|---|---|---|---|---|---|---|---|---|
00 | 00 | 01 | 02 | 10 | 11 | 12 | 20 | 21 | 22 |
01 | 01 | 02 | 00 | 11 | 12 | 10 | 21 | 22 | 20 |
02 | 02 | 00 | 01 | 12 | 10 | 11 | 22 | 20 | 21 |
10 | 10 | 11 | 12 | 20 | 21 | 22 | 00 | 01 | 02 |
11 | 11 | 12 | 10 | 21 | 22 | 20 | 01 | 02 | 00 |
12 | 12 | 10 | 11 | 22 | 20 | 21 | 02 | 00 | 01 |
20 | 20 | 21 | 22 | 00 | 01 | 02 | 10 | 11 | 12 |
21 | 21 | 22 | 20 | 01 | 02 | 00 | 11 | 12 | 10 |
22 | 22 | 20 | 21 | 02 | 00 | 01 | 12 | 10 | 11 |