In this paper, we construct some new (extended) generalized Reed-Solomon (GRS) codes with arbitrary dimensions of Galois hulls. For some special cases, we propose a mechanism. Precisely, these special classes of GRS codes with Galois hulls of arbitrary dimensions can be constructed from GRS codes satisfying Euclidean orthogonal property. Finally, we construct several new families of MDS entanglement-assisted quantum error-correcting codes (EAQECCs) utilizing the above GRS codes with Galois hulls of arbitrary dimensions.
翻译：在本文中,我们制定了一些新的(扩展的)通用Reed-Solomon(GRS)编码,其中含有加罗伊斯船体的任意尺寸。对于某些特殊的情况,我们建议了一个机制。确切地说,Glois船体具有任意尺寸的这些特殊类别的GRS编码,可以用满足Euclidean 正方形财产的GRS编码来构建。最后,我们利用上述Glois船体的GRS编码,建立了几个新的MDS缠绕辅助量子误差校准编码(EAQECCs),与Glois船体具有任意尺寸的Galois船体的GRS编码。
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