Perfect matrix

In mathematics, a perfect matrix is an m-by-n binary matrix which has no possible k-by-k submatrix K which 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:

${\begin{bmatrix}1&1&0&0&0\\0&1&1&0&0\\0&0&1&1&0\\0&0&0&1&1\\1&0&0&0&1\end{bmatrix}}.$