A code $C = \Phi(\mathcal{C})$ is called $\mathbb{Z}_p \mathbb{Z}_{p^2}$-linear if it's the Gray image of the $\mathbb{Z}_p \mathbb{Z}_{p^2}$-additive code $\mathcal{C}$. In this paper, the rank and the dimension of the kernel of $\mathcal{C}$ are studied. Both of the codes $\langle \Phi(\mathcal{C}) \rangle$ and $\ker(\Phi(\mathcal{C}))$ are proven $\mathbb{Z}_p \mathbb{Z}_{p^2}$-additive cyclic codes, and their generator polynomials are determined. Finally, accurate values of rank and the dimension of the kernel of some classes of $\mathbb{Z}_p \mathbb{Z}_{p^2}$-additive cyclic codes are considered.
翻译：代码 $C =\ phexcal{C} = \ mathbb} p\ mathbb} p\ 2} $- 线形 $\ mathbb} p\ mathbb} p\ 2} $- adtive 代码 $\ mathcal{C} 的灰色图像 $\ mathcal =\ mathcal{C} 。 本文研究了 $\ langle \ mathb} p\ mathcal} \ rangle$ 和 $\ ker (\\ mathcal{ c} ) $\ mathbb\ p\ p\ p\ p\ 2} $- aditivitive cycolcol 代码 $\ mathb} 确定 。 最后, 将考虑 $\ mathbp\\\\\\ \\\\ mathb\\\\\\\\\\ 2} $ advichecolc colc codec code 的准确值和大小。
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