By generalizing the stabilizer quantum error-correcting codes, entanglement-assisted quantum error-correcting (EAQEC) codes were introduced, which could be derived from any classical linear codes via the relaxation of self-orthogonality conditions with the aid of pre-shared entanglement between the sender and the receiver. In this paper, three classes of entanglement-assisted quantum error-correcting maximum-distance-separable (EAQMDS) codes are constructed through generalized Reed-Solomon codes. Under our constructions, the minimum distances of our EAQMDS codes are much larger than those of the known EAQMDS codes of the same lengths that consume the same number of ebits. Furthermore, some of the lengths of the EAQMDS codes are not divisors of $q^2-1$, which are completely new and unlike all those known lengths existed before.

翻译：通过推广稳定子量子纠错码，引入了纠缠辅助量子纠错（EAQEC）码。这类码可借助发送方与接收方之间预共享的纠缠，放宽自正交性条件，从而从任意经典线性码中导出。本文利用广义Reed-Solomon码构造了三类纠缠辅助量子纠错最大距离可分（EAQMDS）码。在我们的构造下，这些EAQMDS码的最小距离远大于已知的、消耗相同ebit数量的等长EAQMDS码的最小距离。此外，部分EAQMDS码的长度并非$q^2-1$的因子，这在性质上是全新的，与先前已知的所有长度均不相同。