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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

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