Let's supose that C is the code which contain all the words from $\mathbb{Z}_2^n$ that has a pair number of $1$'s. Which are the C parameters?
Testing in some $n$ I got that for any $n$ we have (n,$2^{n-1}$,2). The longitued of the words and the C distance is obvious, but I don't know how to prove that the amount of words is $2^{n-1}$. Any idea?