most recent 30 from http://mathoverflow.net 2013-06-20T00:08:38Z http://mathoverflow.net/feeds/question/58247 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/58247/minimal-count-of-linear-dependent-columns-in-matrix-tensor-product spk 2011-03-12T08:56:22Z 2011-03-12T08:56:22Z

<p>Hello, all!</p> <p>I have two matrices $\underset{n \times m}{A}$ and $\underset{t \times l}{B}$ over some extension field $GF(2^r)$: $n &lt; m$ and $t &lt; l$. For $A$ minimum count of linear dependent over $GF(2)$ columns is $\tilde{n}$. For $B$ minimum count of linear dependent over $GF(2)$ columns is $\tilde{l}$. Does there exist any solution for a problem, what lower bound for minimum count of linear dependent over $GF(2)$ columns is in $A \otimes B$? $\otimes$ is tensor product.</p> <p>Thank you!</p>