论文标题
来自混合字母和MacWilliams身份的添加剂constacyclic代码的量子代码
Quantum Codes from additive constacyclic codes over a mixed alphabet and the MacWilliams identities
论文作者
论文摘要
令$ \ mathbb {z} _p $为整数ring ring a modulo a Prime $ p $其中$ p-1 $是二次残基modulo $ p $。本文介绍了链环上的constacyclic代码的研究$ \ MATHCAL {r} = \ frac {\ Mathbb {z} _p [u]} {\ langle u^2 \ rangle} $和$ \ natcal { u^3 \ rangle} $。我们还通过$ \ Mathcal {r} \ Mathcal {s} $和$ \ Mathbb {z} _p \ Mathcal {r} \ Mathcal {s} $使用生成器多务本的$ \ Mathcal $ \ \ r} $ {此外，通过在$ \ Mathcal {r} $，$ \ Mathcal {s} $和$ \ Mathbb {z} _p \ Mathcal {r} \ Mathcal {s}上定义灰色地图，我们在附加代码的灰色图像上获得了一些结果。然后，我们给出重量枚举，MacWilliams身份与$ \ Mathbb {z} _p \ Mathcal {r} \ Mathcal {s} $相对应。最后，作为获得的代码的应用，我们使用CSS构造提供了量子代码。
Let $\mathbb{Z}_p$ be the ring of integers modulo a prime number $p$ where $p-1$ is a quadratic residue modulo $p$. This paper presents the study of constacyclic codes over chain rings $\mathcal{R}=\frac{\mathbb{Z}_p[u]}{\langle u^2\rangle}$ and $\mathcal{S}=\frac{\mathbb{Z}_p[u]}{\langle u^3\rangle}$. We also study additive constacyclic codes over $\mathcal{R}\mathcal{S}$ and $\mathbb{Z}_p\mathcal{R}\mathcal{S}$ using the generator polynomials over the rings $\mathcal{R}$ and $\mathcal{S},$ respectively. Further, by defining Gray maps on $\mathcal{R}$, $\mathcal{S}$ and $\mathbb{Z}_p\mathcal{R}\mathcal{S},$ we obtain some results on the Gray images of additive codes. Then we give the weight enumeration and MacWilliams identities corresponding to the additive codes over $\mathbb{Z}_p\mathcal{R}\mathcal{S}$. Finally, as an application of the obtained codes, we give quantum codes using the CSS construction.
