论文标题
$ \ mathbb {z} _p \ mathbb {z} _ {p^2} $ - 线性代码：等级和内核
$\mathbb{Z}_p\mathbb{Z}_{p^2}$-linear codes: rank and kernel
论文作者
论文摘要
代码$ c $称为$ \ z_p \ z_ {p^2} $ - 线性如果是$ \ z_p \ z__ {p^2} $ - 加法代码，其中$ p> 2 $是prime。在本文中，研究了$ \ z_p \ z_ {p^2} $ - 线性代码的秩和维度。 $ \ z_3 \ z_ {9} $ - 线性代码和$ \ z_p \ z__ {p^2} $ - 线性代码的尺寸的两个范围。对于这些界限的每个值，我们为相应的代码提供了详细的构造。最后，还考虑了$ \ z_3 \ z_ {9} $ - 线性代码的成对的等级和尺寸。
A code $C$ is called $\Z_p\Z_{p^2}$-linear if it is the Gray image of a $\Z_p\Z_{p^2}$-additive code, where $p>2$ is prime. In this paper, the rank and the dimension of the kernel of $\Z_p\Z_{p^2}$-linear codes are studied. Two bounds of the rank of a $\Z_3\Z_{9}$-linear code and the dimension of the kernel of a $\Z_p\Z_{p^2}$-linear code are given, respectively. For each value of these bounds, we give detailed construction of the corresponding code. Finally, pairs of rank and the dimension of the kernel of $\Z_3\Z_{9}$-linear codes are also considered.
