Bounds on MLDR Codes Over ${\mathbb Z}_{p^t}$

TL;DR

This paper establishes new upper bounds on the minimum Lee distance of linear codes over ${ m Z}_{p^t}$, introducing the concept of MLDR codes and improving existing bounds using combinatorial methods.

Contribution

It presents novel bounds on MLDR codes over ${ m Z}_{p^t}$, enhancing the understanding of their distance properties and providing tighter constraints than previous results.

Findings

New bounds on MLDR codes derived

Improved upper bounds over existing literature

Use of combinatorial arguments for bounds

Abstract

Upper bounds on the minimum Lee distance of codes that are linear over ${\mathbb Z}_q$, $q=p^t$, $p$ prime are discussed. The bounds are Singleton like, depending on the length, rank, and alphabet size of the code. Codes meeting such bounds are referred to as Maximum Lee Distance with respect to Rank (MLDR) Codes. We present some new bounds on MLDR codes, using combinatorial arguments. In the context of MLDR codes, our work provides improvements over existing bounds in the literature