Problem $1$: Block code is defined by Table $1$

Table $1$:

$\begin{array}{cc}\text{I}\text{n}\text{f}\text{o}\text{r}\text{m}\text{a}\text{t}\text{i}\text{o}\text{n}\text{w}\text{o}\text{r}\text{d}& \text{C}\text{o}\text{d}\text{e}\text{w}\text{o}\text{r}\text{d}\\ 000& 00000\\ 001& 110011\\ 010& 10110\\ 011& 01101\\ 100& 010001\\ 101& 10010\\ 110& 111111\\ 111& 00100\end{array}$

A$.$ Find the code rate. Is it a linear code? If yes, find its generator matrix.

B$.$ Write all code words and draw the corresponding weight $($distribution$)$ spectrum. Is it possible from it to find the code capability to correct the errors?

C$.$ Find a standard array of a code.

D$.$ Is the generator matrix of the code unique?

E$.$ Form some code equivalent to the original code.

F$.$ By changing one code word form a nonlinear block code.