论文标题
GRS代码的新Galois船体和EAQECC的应用
New Galois Hulls of GRS Codes and Application to EAQECCs
论文作者
论文摘要
线性代码的Galois船体在量子编码理论中具有重要的应用。在本文中，我们构建了一些新的（扩展）广义的芦苇 - 固体（GRS）代码，并具有任意维度的Galois船体。我们还提出了一种使用特殊欧几里得正交GRS代码的任意维度的Galois船体构建GRS代码的一般方法。最后，我们通过利用上述结果来构建几个纠缠辅助量子误差校正代码（EAQECC）和MDS EAQECC的新家族。
Galois hulls of linear codes have important applications in quantum coding theory. In this paper, we construct some new classes of (extended) generalized Reed-Solomon (GRS) codes with Galois hulls of arbitrary dimensions. We also propose a general method on constructing GRS codes with Galois hulls of arbitrary dimensions from special Euclidean orthogonal GRS codes. Finally, we construct several new families of entanglement-assisted quantum error-correcting codes (EAQECCs) and MDS EAQECCs by utilizing the above results.
