  We describe a decisional attack against a version of the PLWE problem in
which the samples are taken from a certain proper subring of large dimension of
the cyclotomic ring $\mathbb{F}_q[x]/(\Phi_{p^k}(x))$ with $k>1$ in the case
where $q\equiv 1\pmod{p}$ but $\Phi_{p^k}(x)$ is not totally split over
$\mathbb{F}_q$. Our attack uses the fact that the roots of $\Phi_{p^k}(x)$ over
suitable extensions of $\mathbb{F}_q$ have zero-trace and has overwhelming
success probability as a function of the number of input samples. An
implementation in Maple and some examples of our attack are also provided.
