论文标题
美元
$\mathbb{Z}_p\mathbb{Z}_{p^2}$-additive cyclic codes: kernel and rank
论文作者
论文摘要
代码$ c =φ（\ MATHCAL {C}）$称为$ \ MATHBB {Z} _p \ Mathbb {Z} _ {p^2} $ - 线性如果是$ \ Mathbb {z} _p {zp \ mathbb {z mathbb {z} {z} $ {p^$ {p^$ {p^p^$ {p^p^$ {p^p^$ {c {c {p^2}，则是线性的。在本文中，研究了$ \ Mathcal {C} $的内核的等级和尺寸。这两个代码$ \langleφ（\ Mathcal {c}）\ rangle $和$ \ ker（φ（\ Mathcal {c}））$均已证明$ \ MATHBB {z} _p {z} _p \ Mathbb {z} _ {z} _ {z} _ {p^2} $ - 添加了cynom，并确定了polotitial cyers and polotitation and copitator。最后，考虑了$ \ mathbb {z} _p \ mathbb {z} _ {p^2} $ - 添加循环代码的某些类别的准确值和某些类的内核维度。
A code $C = Φ(\mathcal{C})$ 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 $\langle Φ(\mathcal{C}) \rangle$ and $\ker(Φ(\mathcal{C}))$ 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.
