论文标题
$ \ mathbb {z} _p \ mathbb {z} _ {p^2} $ - 线性代码
Rank and pairs of Rank and Dimension of Kernel of $\mathbb{Z}_p\mathbb{Z}_{p^2}$-linear codes
论文作者
论文摘要
代码$ c $称为$ \ mathbb {z} _p \ mathbb {z} _ {p^2} $ - 如果是$ \ mathbb {z} _p \ mathbb {z} _ {z} _ {p^2} $ - 添加性代码，则是线性的。对于任何质数$ p $大于$ 3 $，$ \ mathbb {z} _p \ mathbb {z} _ {p^2} $ - 线性代码的等级的边界。对于等级的每个值和排名对以及$ \ mathbb {z} _p \ mathbb {z} _ {p^2} $ - 线性代码的内核的尺寸，我们提供了相应代码的详细构造。最后，研究了$ \ mathbb {z} _5 \ mathbb {z} _ {25} $线性代码的级别和尺寸。
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. For any prime number $p$ larger than $3$, the bounds of the rank of $\mathbb{Z}_p\mathbb{Z}_{p^2}$-linear codes are given. For each value of the rank and the pairs of rank and the dimension of the kernel of $\mathbb{Z}_p\mathbb{Z}_{p^2}$-linear codes, we give detailed construction of the corresponding codes. Finally, as an example, the rank and the dimension of the kernel of $\mathbb{Z}_5\mathbb{Z}_{25}$-linear codes are studied.
