Let $\mathcal{C}$ be a quasi-cyclic code of index $l(l\geq2)$. Let $G$ be the subgroup of the automorphism group of $\mathcal{C}$ generated by $\rho^l$ and the scalar multiplications of $\mathcal{C}$, where $\rho$ denotes the standard cyclic shift. In this paper, we find an explicit formula of orbits of $G$ on $\mathcal{C}\setminus \{\mathbf{0}\}$. Consequently, an explicit upper bound on the number of nonzero weights of $\mathcal{C}$ is immediately derived and a necessary and sufficient condition for codes meeting the bound is exhibited. If $\mathcal{C}$ is a one-generator quasi-cyclic code, a tighter upper bound on the number of nonzero weights of $\mathcal{C}$ is obtained by considering a larger automorphism subgroup which is generated by the multiplier, $\rho^l$ and the scalar multiplications of $\mathcal{C}$. 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}.

翻译：设 $\mathcal{C}$ 是索引为 $l(l\geq2)$ 的准循环码。令 $G$ 为由 $\rho^l$ 和 $\mathcal{C}$ 的标量乘法生成的 $\mathcal{C}$ 自同构群子群，其中 $\rho$ 表示标准循环移位。本文给出了 $G$ 在 $\mathcal{C}\setminus \{\mathbf{0}\}$ 上的轨道显式公式。由此直接推导出 $\mathcal{C}$ 的非零重量数的显式上界，并给出了达到该上界的码的充要条件。若 $\mathcal{C}$ 为单生成子准循环码，则考虑由乘子、$\rho^l$ 和 $\mathcal{C}$ 的标量乘法生成的更大自同构子群，可获得 $\mathcal{C}$ 非零重量数的更紧上界。特别地，我们列举若干实例证明该上界的紧致性。主要结果改进并推广了文献 \cite{M2} 中的部分结论。