论文标题
量子MDS代码的结构
Constructions of quantum MDS codes
论文作者
论文摘要
令$ \ mathbb {f} _q $为有限字段，$ q = p = p^{e} $ elements，其中$ p $是质量数字，$ e \ geq 1 $是整数。在本文中，通过广义的芦苇 - 溶剂（GRS）代码，我们构建了两个新类别的量子最大距离 - 距离分离（量子MDS）代码，该代码具有参数 $ $ [[q+1，2k-q-1，q-k+2]] _ q $$对于$ \ lceil \ frac \ frac {q+2} {2} {2} \ rceil \ leq k \ leq k \ leq q+1 $，和$ $ \ lceil \ frac {n} {2} \ rceil \ leq k \ leq n $。我们的结构改善并推广了文献中可用的一些结果。此外，我们对Fang等人提出的开放问题给出了肯定的答案。在\ cite {fang1}中。
Let $\mathbb{F}_q$ be a finite field with $q=p^{e}$ elements, where $p$ is a prime number and $e \geq 1$ is an integer. In this paper, by means of generalized Reed-Solomon (GRS) codes, we construct two new classes of quantum maximum-distance-separable ( quantum MDS) codes with parameters $$[[q + 1, 2k-q-1, q-k+2]]_q$$ for $\lceil\frac{q+2}{2}\rceil \leq k\leq q+1$, and $$[[n,2k-n,n-k+1]]_q$$ for $n\leq q $ and $ \lceil\frac{n}{2}\rceil \leq k\leq n$. Our constructions improve and generalize some results of available in the literature. Moreover, we give an affirmative answer to the open problem proposed by Fang et al. in \cite{Fang1}.
