论文标题
通过一般非链环的constacyclic代码的新量子代码
New Quantum codes from constacyclic codes over a general non-chain ring
论文作者
论文摘要
令$ q $为主要力量，让$ \ m nrycal {r} = \ mathbb {f} _ {q} [u_1，u_2，u_2，\ cdots，u_k]/\ langle f_i（u_i），u_iu_iu_j-jj-u_ju_ju_i \ rangle be a a a in-wer-pernon-non-feiq， \ leq k $是多项式，而不是全部线性，它们分为$ \ mathbb {f} _ {q} $上的不同线性因子。我们通过环$ \ Mathcal {r} $表征constacyclic代码，并从中研究量子代码。作为一种应用，与最知名的代码相比，一些新的，更好的量子代码。我们还证明，多项式$ f_i（u_i）的选择，$ 1 \ leq i \ leq k $是无关紧要的，而从$ \ mathcal {r} $上构建量子代码时，它仅取决于其学位。结果表明，量子MDS代码始终存在$ [[n，n-2,2]] _ q $，任何$ n $ a $带有$ \ gcd（n，q）\ neq 1. $。
Let $q$ be a prime power and let $\mathcal{R}=\mathbb{F}_{q}[u_1,u_2, \cdots, u_k]/\langle f_i(u_i),u_iu_j-u_ju_i\rangle$ be a finite non-chain ring, where $f_i(u_i), 1\leq i \leq k$ are polynomials, not all linear, which split into distinct linear factors over $\mathbb{F}_{q}$. We characterize constacyclic codes over the ring $\mathcal{R}$ and study quantum codes from these. As an application, some new and better quantum codes, as compared to the best known codes, are obtained. We also prove that the choice of the polynomials $f_i(u_i),$ $1 \leq i \leq k$ is irrelevant while constructing quantum codes from constacyclic codes over $\mathcal{R}$, it depends only on their degrees. It is shown that there always exists Quantum MDS code $[[n,n-2,2]]_q$ for any $n$ with $\gcd (n,q)\neq 1.$
