In this paper, some new classes of entanglement-assisted quantum MDS codes (EAQMDS codes for short) are constructed via generalized Reed–Solomon codes over finite fields of odd characteristic. Among our constructions, there are many EAQMDS codes with new lengths. The lengths of these EAQMDS codes may not be divisors of \(q^2\pm 1\), which are new and have never been reported.

中文翻译：

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广义Reed–Solomon码的纠缠辅助量子MDS码

在本文中，通过广义Reed-Solomon码在奇特性有限域上构造了一些新的纠缠辅助量子MDS码（简称EAQMDS码）。在我们的结构中，有许多具有新长度的EAQMDS代码。这些EAQMDS代码的长度可能不是\（q ^ 2 \ pm 1 \）的因数，这是新的，从未有过报道。