This paper contributes to k-error linear complexity of some generalized cyclotomic binary sequences of length 2p^m and p^m constructed in recent years. By defining related reference sequences, we find that these sequences possess very low k-error linear complexity for some certain values of the parameter k even though they have high linear complexity. Moreover, we point out that (p-1)-tuple distributions of all these sequences are not span. Thus they should be selected carefully for use in stream cipher systems.