We use invariant theory of finite groups to study shape enumerators of self-dual linear codes in a finite NRT metric space. We provide a new approach that avoids applying Molien's formula to compute all possible shape enumerators. Enhancing existing methods, we describe the shape enumerators of all self-dual NRT codes over an arbitrary finite field.

翻译：我们利用有限群的不变理论研究有限NRT度量空间中自对偶线性码的形状枚举器。我们提出了一种新方法，避免了应用Molien公式计算所有可能的形状枚举器。通过改进现有方法，我们描述了任意有限域上所有自对偶NRT码的形状枚举器。