A code C is called \(\mathbb {Z}_p\mathbb {Z}_{p^2}\)-linear if it is the Gray image of a \(\mathbb {Z}_p\mathbb {Z}_{p^2}\)-additive code, where \(p>2\) is prime. In this paper, the rank and the dimension of the kernel of \(\mathbb {Z}_p\mathbb {Z}_{p^2}\)-linear codes are studied. The range of their values is given. For each value of the rank of \(\mathbb {Z}_p\mathbb {Z}_{p^2}\)-linear codes, we give detailed construction of the corresponding codes. Similarly, for the values of the dimension of the kernel, we also give a construction method. Finally, pairs of rank and the dimension of the kernel of \(\mathbb {Z}_p\mathbb {Z}_{p^2}\)-additive codes are also considered.

A码Ç称为\（\ mathbb {Z} _p \ mathbb {Z} _ {P ^ 2} \） -线性如果是的灰色图像\（\ mathbb {Z} _p \ mathbb {Z} _ {p^2}\) -加法代码，其中\(p>2\)是素数。本文研究了\(\mathbb {Z}_p\mathbb {Z}_{p^2}\)-线性码的核的秩和维数。给出了它们的值的范围。对于\(\mathbb {Z}_p\mathbb {Z}_{p^2}\) -线性代码的秩的每个值，我们给出了相应代码的详细构造。同样，对于核的维度值，我们也给出了构造方法。最后，\(\mathbb {Z}_p\mathbb {Z}_{p^2}\)的核的秩和维数对- 附加代码也被考虑。