Remarks on a cyclotomic sequence

We analyse a binary cyclotomic sequence constructed via generalized cyclotomic classes by Bai {\it et al.} in 2005. First we determine the linear complexity of a natural generalization of this binary sequence to arbitrary prime fields. Secondly we consider $k$-error linear complexity and autocorrelation of these sequences and point out certain drawbacks of this construction. The results show that the parameters for the sequence construction must be carefully chosen in view of the respective application.