  We investigate the $k$-error linear complexity of $p^2$-periodic binary
sequences defined from the polynomial quotients (including the well-studied
Fermat quotients), which is defined by $$ q_{p,w}(u)\equiv \frac{u^w-u^{wp}}{p}
\bmod p ~ \mathrm{with} 0 \le q_{p,w}(u) \le p-1, ~u\ge 0, $$ where $p$ is an
odd prime and $1\le w<p$. Indeed, first for all integers $k$, we determine
exact values of the $k$-error linear complexity over the finite field $\F_2$
for these binary sequences under the assumption of f2 being a primitive root
modulo $p^2$, and then we determine their $k$-error linear complexity over the
finite field $\F_p$ for either $0\le k<p$ when $w=1$ or $0\le k<p-1$ when $2\le
w<p$. Theoretical results obtained indicate that such sequences possess `good'
error linear complexity.
