With entanglement-assisted (EA) formalism, arbitrary classical linear codes are allowed to transform into EAQECCs by using pre-shared entanglement between the sender and the receiver. In this paper, based on classical cyclic MDS codes by exploiting pre-shared maximally entangled states, we construct two families of $q$-ary entanglement-assisted quantum MDS codes $[[\frac{q^{2}+1}{a},\frac{q^{2}+1}{a}-2(d-1)+c,d;c]]$, where q is a prime power in the form of $am+l$, and $a=(l^2+1)$ or $a=\frac{(l^2+1)}{5}$. We show that all of $q$-ary EAQMDS have minimum distance upper limit much larger than the known quantum MDS (QMDS) codes of the same length. Most of these $q$-ary EAQMDS codes are new in the sense that their parameters are not covered by the codes available in the literature.
翻译:以缠绕(EA)的形式,允许任意的古典线性代码使用发件人和接收人之间预先共享的缠绕,转换成EAQECCs。在本文中,根据古典环曲MDS编码,通过利用预先共享的缠绕状态,我们建造了两组$-Q-内缠绕(EA)的量子MDS编码 $[(frac{q ⁇ 2 ⁇ 2 ⁇ 1 ⁇ 1 ⁇ a},\frac{qq ⁇ 2 ⁇ 2 ⁇ 1 ⁇ a}-2(d-1)+c,d;c]$,其中q是美元+l$和$a=2+1美元或$a ⁇ frac{(l ⁇ 2+1)%5}美元的主要动力。我们显示,所有$-QQMDS的最小距离上限大大高于已知的量子MDS(QMDS)编码。这些$q$-y EAQMDS的代码大多是新的,因为它们参数不在文献中。