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Table 1 A quasigroup \((Q,*)\) of order p kd

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

* 0 1 2 \(\ldots\) \(p^{kd}-1\)
0 \(q^{(0)}_0\) \(q^{(0)}_1\) \(q^{(0)}_2\) \(\cdots\) \(q^{(0)}_{p^{kd}-1}\)
1 \(q^{(1)}_0\) \(q^{(1)}_1\) \(q^{(1)}_2\) \(\cdots\) \(q^{(1)}_{p^{kd}-1}\)
2 \(q^{(2)}_0\) \(q^{(2)}_1\) \(q^{(2)}_2\) \(\cdots\) \(q^{(2)}_{p^{kd}-1}\)
\(\vdots\) \(\vdots\) \(\vdots\) \(\vdots\) \(\vdots\) \(\vdots\)
\(p^{kd}-1\) \(q^{(p^{kd}-1)}_0\) \(q^{(p^{kd}-1)}_1\) \(q^{(p^{kd}-1)}_2\) \(\cdots\) \(q^{(p^{kd}-1)}_{p^{kd}-1}\)