Some Notes on the Generalized Cyclotomic Binary Sequences of Length 2pm and pm

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.