Abstract In 1997, Shor and Laflamme defined weight enumerators for quantum error-correcting codes and derived a MacWilliams identity. Recently, we proposed two new notions, the double weight enumerators and complete weight enumerators, for binary quantum codes. Now we will extend these results to nonbinary quantum codes. Based on the MacWilliams identities for these enumerators, we explicitly determine the Singleton-type and Hamming-type bounds for arbitrary nonbinary asymmetric quantum codes.

中文翻译：

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非二元非对称量子码的权重枚举器及其应用

摘要 1997 年，Shor 和 Laflamme 定义了量子纠错码的权重枚举器，并导出了 MacWilliams 恒等式。最近，我们提出了两个新的概念，双权重枚举器和完全权重枚举器，用于二进制量子代码。现在我们将这些结果扩展到非二进制量子代码。基于这些枚举器的 MacWilliams 恒等式，我们明确地确定了任意非二进制非对称量子代码的单例型和汉明型界限。