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 \( \left[\left[\frac{q^2+1}{a},\frac{q^2+1}{a}-2\left(d-1\right)+c,d;c\right]\right] \), where q is a prime power in the form of am + l, and a = (l² + 1) or \( a=\frac{\left({l}^2+1\right)}{5} \). 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.

使用纠缠辅助（EA）形式，通过使用发送者和接收者之间的预共享纠缠，可以将任意经典线性代码转换为EAQECC。在本文中，我们基于经典循环MDS代码，通过利用预共享的最大纠缠态，构造了两族q元纠缠辅助量子MDS代码\（\ left [\ left [\ frac {q ^ 2 + 1} {a}，\ frac {q ^ 2 + 1} {a} -2 \ left（d-1 \ right）+ c，d; c \ right] \ right] \），其中q是的形式上午 + 升，和一个 =（升²  + 1）或\（A = \压裂{\左（{1} ^ 2 + 1 \右）} {5} \） 。我们证明所有的q一元EAQMDS的最小距离上限远大于相同长度的已知量子MDS（QMDS）码。这些q元EAQMDS代码中的大多数都是新的，因为它们的参数未包含在文献中的代码中。