Better bounds on the minimal Lee distance

TL;DR

This paper introduces new bounds on the minimum Lee distance of codes over integer residue rings, using novel definitions of generalized Lee weights and support types, advancing the theoretical understanding of Lee metric codes.

Contribution

It proposes three new support types and a new perspective on generalized weights, leading to improved Singleton-like bounds for Lee metric codes.

Findings

Derived new bounds on Lee distance using novel support concepts

Analyzed the utility of different support types for code bounds

Discussed the density of maximum Lee distance codes relative to new bounds

Abstract

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.