Generator matrix of $E_5$ 
Let $E_5$ denote the binary even weight code of length 5. Write down a generator matrix of $E_5$.

So I know the length $n = 5$ is the number of rows in the generator matrix and the number of columns will be the dimension of $E_5$.
So I firstly need to know how to work out the dimension and I can then attempt to construct the generator matrix. Please can someone give me a hint!

Think of how many degrees of freedom you have for this code.  How many bits can you fill in however you want, and still be able to use the remaining bits to make the word "even"?
