  Recently, Blanco-Chac\'on proved the equivalence between the Ring Learning
With Errors and Polynomial Learning With Errors problems for some families of
cyclotomic number fields by giving some upper bounds for the condition number
$\operatorname{Cond}(V_n)$ of the Vandermonde matrix $V_n$ associated to the
$n$th cyclotomic polynomial. We prove some results on the singular values of
$V_n$ and, in particular, we determine $\operatorname{Cond}(V_n)$ for $n = 2^k
p^\ell$, where $k, \ell \geq 0$ are integers and $p$ is an odd prime number.
