In this paper, a family of new entanglement-assisted quantum error-correcting codes (EAQECCs) is constructed from constacyclic codes with length \(n=\frac{q^2+1}{a}\) by giving a new method to select defining sets, where \(a=m^2+1\), \(m>2\) is even and q is an odd prime power with \(a\mid (q\pm m)\). It is worth pointing out that those EAQECCs are entanglement-assisted quantum maximum distance separable (EAQMDS) codes when \(d\le \frac{n+2}{2}\). All of them are new in the sense that their parameters are not covered by the previously known ones. Moreover, they have minimum distance larger than \(q+1\). Compared with the codes with the same length listed in Table 1, our codes have larger minimum distance.

在本文中，一系列新的纠缠辅助量子纠错码（EAQECCs）由长度为\(n=\frac{q^2+1}{a}\)的恒环码通过给出一种新的方法来构造选择定义集，其中\(a=m^2+1\)，\(m>2\)是偶数，q是与\(a\mid (q\pm m)\)的奇数次幂。值得指出的是，当\(d\le \frac{n+2}{2}\)时，那些 EAQECC 是纠缠辅助量子最大距离可分 (EAQMDS) 代码。所有这些都是新的，因为它们的参数没有被先前已知的参数覆盖。此外，它们的最小距离大于\(q+1\). 与表1中列出的相同长度的代码相比，我们的代码具有更大的最小距离。