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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