Solution
= Solution
If $c\in C$ had odd <Hamming weight>, add all $n$ cyclic shifts of $c$. Each coordinate of the sum is the sum of all coordinates of $c$, namely one in $\mathbb F_2$. Linearity and cyclicity would therefore put $(1,\ldots,1)$ in $C$, contrary to the hypothesis. Hence every codeword has even weight.