Matching a binary matrix - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T07:46:12Z http://mathoverflow.net/feeds/question/96057 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/96057/matching-a-binary-matrix Matching a binary matrix Chong Luo 2012-05-05T10:16:17Z 2012-05-07T10:03:06Z <p>Given a MxN 0-1 matrix D, with the property that </p> <ol> <li>both M and N are odd numbers</li> <li>its row sums and column sums in the $\mathbb{Z}_2$ field are all equal to the same number (0 or 1).</li> </ol> <p>How do we find M binary numbers $r_i$ and N binary numbers $c_j$, such that $\sum r_i = \sum c_j$ and $$r_i + c_j = D_{ij}$$ is satisfied for as many cell $(i,j)$ as possible? (By the way, the "+" is in the $\mathbb{Z}_2$ field, that is the XOR operation.)</p>