We provide an attack against the decision version of PLWE over the cyclotomic
ring $mathbb{F}_q[x]/(Phi_{p^k}(x))$ with $k>1$ in the case where $qequiv
1pmod{p}$ but $Phi_{p^k}(x)$ is not totally split over $mathbb{F}_q$. Our
attack uses that the roots of $Phi_{p^k}(x)$ over suitable extensions of
$mathbb{F}_q$ have zero-trace and has overwhelming success probability in
function of the number of samples taken as input. An implementation in Maple
and some examples of our attack are also provided.

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