On error linear complexity of new generalized cyclotomic binary sequences of period $p^2$

We consider the $k$-error linear complexity of a new binary sequence of period $p^2$, proposed in the recent paper "New generalized cyclotomic binary sequences of period $p^2$", by Z. Xiao et al., who calculated the linear complexity of the sequences (Designs, Codes and Cryptography, 2017, https://doi.org/10.1007/s10623-017-0408-7). More exactly, we determine the values of $k$-error linear complexity over $\mathbb{F}_2$ for almost $k>0$ in terms of the theory of Fermat quotients. Results indicate that such sequences have good stability.