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Table 2 A quasigroup \((Q,*)\) of order 24 and its representations based on \(GF(2^2)\)

From: An algorithm for judging and generating multivariate quadratic quasigroups over Galois fields

* 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 0 3 2 5 4 7 6 9 8 11 10 13 12 15 14
2 2 3 0 1 6 7 4 5 10 11 8 9 14 15 12 13
3 3 2 1 0 7 6 5 4 11 10 9 8 15 14 13 12
4 4 5 6 7 0 1 2 3 12 13 14 15 8 9 10 11
5 5 4 7 6 1 0 3 2 13 12 15 14 9 8 11 10
6 6 7 4 5 2 3 0 1 14 15 12 13 10 11 8 9
7 7 6 5 4 3 2 1 0 15 14 13 12 11 10 9 8
8 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7
9 9 8 11 10 13 12 15 14 1 0 3 2 5 4 7 6
10 10 11 8 9 14 15 12 13 2 3 0 1 6 7 4 5
11 11 10 9 8 15 14 13 12 3 2 1 0 7 6 5 4
12 12 13 14 15 8 9 10 11 4 5 6 7 0 1 2 3
13 13 12 15 14 9 8 11 10 5 4 7 6 1 0 3 2
14 14 15 12 13 10 11 8 9 6 7 4 5 2 3 0 1
15 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
* 00 01 02 03 10 11 12 13 20 21 22 23 30 31 32 33
00 00 01 02 03 10 11 12 13 20 21 22 23 30 31 32 33
01 01 00 03 02 11 10 13 12 21 20 23 22 31 30 33 32
02 02 03 00 01 12 13 10 11 22 23 20 21 32 33 30 31
03 03 02 01 00 13 12 11 10 23 22 21 20 33 32 31 30
10 10 11 12 13 00 1 02 03 30 31 32 33 20 21 22 23
11 11 10 13 12 01 0 03 02 31 30 33 32 21 20 23 22
12 12 13 10 11 02 03 00 01 32 33 30 31 22 23 20 21
13 13 12 11 10 03 02 01 00 33 32 31 30 23 22 21 20
20 20 21 22 23 30 31 32 33 00 01 02 03 10 11 12 13
21 21 20 23 22 31 30 33 32 01 00 03 02 11 10 13 12
22 22 23 20 21 32 33 30 31 02 03 00 01 12 13 10 11
23 23 22 21 20 33 32 31 30 03 02 01 00 13 12 11 10
30 30 31 32 33 20 21 22 23 10 11 12 13 00 01 02 03
31 31 30 33 32 21 20 23 22 11 10 13 12 01 00 03 02
32 32 33 30 31 22 23 20 21 12 13 10 11 02 03 00 01
33 33 32 31 30 23 22 21 20 13 12 11 10 03 02 01 00