论文标题
$ \ mathbb {z} _ {p^2} $和$ \ mathbb {z} _p \ mathbb {z} _ {p^2}
Gray Images of Cyclic Codes over $\mathbb{Z}_{p^2}$ and $\mathbb{Z}_p\mathbb{Z}_{p^2}
论文作者
论文摘要
在本文中，我们首先研究$ \ mathbb {z} _p \ mathbb {z} _ {p^k} $ - 添加循环代码的代数结构，并提供生成器的多项式和这些代码的最小跨度集。其次，对于$ \ mathbb {z} _p \ mathbb {z} _ {p^2} $ - 灰色映像是线性（不一定是循环）$ \ mathbb {z} _p $的添加代码的必要条件。此外，对于某些特殊的循环代码系列$ \ mathbb {z} _ {9} $和$ \ mathbb {z} _3 \ mathbb {z} _ {9} $，确定了灰色图像的线性。
In the paper, we firstly study the algebraic structures of $\mathbb{Z}_p \mathbb{Z}_{p^k}$-additive cyclic codes and give the generator polynomials and the minimal spanning set of these codes. Secondly, a necessary and sufficient condition for a class of $\mathbb{Z}_p\mathbb{Z}_{p^2}$-additive codes whose Gray images are linear (not necessarily cyclic) over $\mathbb{Z}_p$ is given. Moreover, as for some special families of cyclic codes over $\mathbb{Z}_{9}$ and $\mathbb{Z}_3 \mathbb{Z}_{9}$, the linearity of the Gray images is determined.
