  We investigate the $k$-error linear complexity of pseudorandom binary
sequences of period $p^{\mathfrak{r}}$ derived from the Euler quotients modulo
$p^{\mathfrak{r}-1}$, a power of an odd prime $p$ for $\mathfrak{r}\geq 2$.
When $\mathfrak{r}=2$, this is just the case of polynomial quotients (including
Fermat quotients) modulo $p$, which has been studied in an earlier work of
Chen, Niu and Wu. In this work, we establish a recursive relation on the
$k$-error linear complexity of the sequences for the case of $\mathfrak{r}\geq
3$. We also state the exact values of the $k$-error linear complexity for the
case of $\mathfrak{r}=3$. From the results, we can find that the $k$-error
linear complexity of the sequences (of period $p^{\mathfrak{r}}$) does not
decrease dramatically for $k<p^{\mathfrak{r}-2}(p-1)^2/2$.
