Cfrgtkky

0 Distribution upgrade to 18.04.01 hangs at Restarting Computer Preparing to configure Libgusb2 (i386) Intel 2 Core 1.68 2 GB 18.04 upgrade share | improve this question edited Nov 30 at 7:41 Zanna 50k 13 131 238 asked Nov 29 at 22:06 bobk 1 1 add a comment  |  ...

0 For simplicity, assume $n$ and $w$ are even. Let $mathbf{M} in mathbb{F}_2^{n times m}$ be an arbitrary matrix with $operatorname{rank} mathbf{M} = w$ . What is the probability that we can write $$ mathbf{M} = begin{bmatrix} mathbf{M}_1 \ mathbf{M}_2 end{bmatrix}text, $$ where $mathbf{M}_1, mathbf{M}_2 in mathbb{F}_2^{(n / 2) times m}$ and $operatorname{rank} mathbf{M}_1 = operatorname{rank} mathbf{M}_2 = w / 2$ ? What follows is what I have worked on so far. There are (see 1) $$ C := binom{n}{w}_2 prod_{i = 0}^{w - 1} left(2^m - 2^iright) $$ choices for $mathbf{M}$ , where $binom{n}{w}_2$ denotes the $2$ -binomial coefficient. Given some $mathbf{M}_2$ with $operatorname{rank} mathbf{M}_2 = w / 2$ , the number of ways we can "extend" it (as per problem statement) by an $mathb...