This paper provides new and improved Singleton-like bounds for Lee metric codes over integer residue rings. We derive the bounds using various novel definitions of generalized Lee weights based on different notions of a support of a linear code. In this regard, we introduce three main different support types for codes in the Lee metric and analyze their utility to derive bounds on the minimum Lee distance. Eventually, we propose a new point of view to generalized weights and give an improved bound on the minimum distance of codes in the Lee metric for which we discuss the density of maximum Lee distance codes with respect to this novel Singleton-like bound.

翻译：本文给出了整数剩余环上李度量码新的、改进的Singleton型界。我们基于线性码支撑的不同概念，利用多种新定义的广义李权重推导出这些界。为此，我们针对李度量中的码引入了三种主要的不同支撑类型，并分析了它们在推导最小李距离界时的效用。最终，我们提出了广义权重的新视角，并给出了李度量中码的最小距离的一个改进界，同时讨论了最大李距离码相对于这一新型Singleton型界的密度。