Let C be a quasi-cyclic code of index l(lβ₯2). Let G be the
subgroup of the automorphism group of C generated by Οl and
the scalar multiplications of C, where Ο denotes the standard
cyclic shift. In this paper, we find an explicit formula of orbits of G on
Cβ{0}. Consequently, an explicit upper bound on
the number of non-zero weights of C is immediately derived and a
necessary and sufficient condition for codes meeting the bound is exhibited. In
particular, we list some examples to show the bounds are tight. Our main result
improves and generalizes some of the results in \cite{M2}