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In mathematics, a perfect matrix is an m-by-n binary matrix that has no possible k-by-k submatrix K that satisfies the following conditions:

• k > 3
• the row and column sums of K are each equal to b, where b ≥ 2
• there exists no row of the (m − k)-by-k submatrix formed by the rows not included in K with a row sum greater than b.

The following is an example of a K submatrix where k = 5 and b = 2:

$\left[\begin{array}{ccccc}1& 1& 0& 0& 0\\ 0& 1& 1& 0& 0\\ 0& 0& 1& 1& 0\\ 0& 0& 0& 1& 1\\ 1& 0& 0& 0& 1\end{array}\right].$

References

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