$V^5$ is the set of length $5$ codewords. $V^5[x] = \mathbb F_2[x]/ \langle x^5-1\rangle $.
Show that the ideal $\langle 1+x \rangle$ in $V^5[x]$ corresponds to the code in $V^5$ with all words of even weight.
Of course, one way of doing this is generating an ideal with $ 1+x $, but this is obviously quite time consuming. I believe the homework problem has a more efficient solution...but I can't think of anything. Any ideas?