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.
翻译：线性编码的伽洛瓦船体在量子编码理论中具有重要应用。在本文中,我们用任意尺寸的加罗瓦船体构建了一些新的(扩展的)通用Reed-Solomon(GRS)编码,我们还提出了一个一般性方法,利用上述结果,用Euclidean orthogonal GRS特殊编码来构建Glois船体任意尺寸的Glois船体的Greed-Solomon(GRS)编码。最后,我们用上述结果构建了几组新的缠绕辅助量子校准码(EAQECCs)和MDS EAQECCs的混合量子校准码(EAQECCs)和MDS EAQECCs(EAQECCs)。
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