论文标题
来自环constacyclic代码的新的非二进制量子代码在环上$ \ mathbb {f} _ {p^m}+v \ mathbb {f} _ {p^m}+v^2 \ mathbb {f}
New non-binary quantum codes from skew constacyclic codes over the ring $\mathbb{F}_{p^m}+v\mathbb{F}_{p^m}+v^2 \mathbb{F}_{p^m}$
论文作者
论文摘要
在本文中，我们通过有限的交换性非链环$ \ Mathcal {r} = \ Mathbb {f} _ {p^m} [v]/\ langle v^3 = v \ rangle $ p $ od prime和$ m m \ geq 1 $ m m \ geq 1 $ m m \ geq。为了获得此类量子代码，首先，我们研究偏斜constacyclic代码及其在环$ \ Mathcal {r} $上的欧几里得双重的结构属性。然后，建立了在$ \ Mathcal {r} $上偏斜constacyclic代码的必要条件，以包含其欧几里得双重。最后，借助CSS构建和使用灰色地图，许多新的非二进制量子代码是通过$ \ Mathbb {f} _ {p^m} $获得的。
In this article, we construct new non-binary quantum codes from skew constacyclic codes over finite commutative non-chain ring $\mathcal{R}= \mathbb{F}_{p^m}[v]/\langle v^3 =v \rangle$ where $p$ is an odd prime and $m \geq 1$. In order to obtain such quantum codes, first we study the structural properties of skew constacyclic codes and their Euclidean duals over the ring $\mathcal{R}$. Then a necessary and sufficient condition for skew constacyclic codes over $\mathcal{R}$ to contain their Euclidean duals is established. Finally, with the help of CSS construction and using Gray map, many new non-binary quantum codes are obtained over $\mathbb{F}_{p^m}$.
