论文标题
从广义的芦苇 - 固体代码中的纠缠辅助量子MDS代码的结构
Constructions of entanglement-assisted quantum MDS codes from generalized Reed-Solomon codes
论文作者
论文摘要
通过概括稳定器量子误差校正代码，引入了纠缠辅助量子误差校正（EAQEC）代码，这可以通过在发送者和接收器之间的预共享范围内放松自我实行条件来从任何经典线性代码中得出。在本文中，三类纠缠量的量子误差校正最大距离分离（EAQMDS）代码是通过广义的Reed-Solomon代码构建的。在我们的构造下，我们的EAQMDS代码的最小距离要比消耗相同数量的EBIT的相同长度的已知EAQMDS代码的最小距离要大得多。此外，EAQMDS代码的某些长度不是$ q^2-1 $的除数，它们是全新的，与以前存在的所有已知长度不同。
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.
