This website requires JavaScript.

Quantum Codes from additive constacyclic codes over a mixed alphabet and the MacWilliams identities

Indibar DebnathAshutosh SinghOm PrakashAbdollah Alhevaz
Dec 2022
摘要
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 ofconstacyclic codes over chain rings $\mathcal{R}=\frac{\mathbb{Z}_p[u]}{\langleu^2\rangle}$ and $\mathcal{S}=\frac{\mathbb{Z}_p[u]}{\langle u^3\rangle}$. Wealso study additive constacyclic codes over $\mathcal{R}\mathcal{S}$ and$\mathbb{Z}_p\mathcal{R}\mathcal{S}$ using the generator polynomials over therings $\mathcal{R}$ and $\mathcal{S},$ respectively. Further, by defining Graymaps 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 theweight enumeration and MacWilliams identities corresponding to the additivecodes over $\mathbb{Z}_p\mathcal{R}\mathcal{S}$. Finally, as an application ofthe obtained codes, we give quantum codes using the CSS construction.
展开全部
图表提取

暂无人提供速读十问回答

论文十问由沈向洋博士提出,鼓励大家带着这十个问题去阅读论文,用有用的信息构建认知模型。写出自己的十问回答,还有机会在当前页面展示哦。

Q1论文试图解决什么问题?
Q2这是否是一个新的问题?
Q3这篇文章要验证一个什么科学假设?
0
被引用
笔记
问答