I don't think that is sufficient: a submatrix need not have all ones, as for example in the 3x3 submatrix of the example. Indeed, a 3x3 submatrix could have bit-patterns 110, 101, 011 such that no two rows or column are the same, nor is any row or column all ones.

Hugo

In reply to Re^2: decomposing binary matrices by hv
in thread decomposing binary matrices by hv

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