On Codes Over $\mathbb{Z}_{p^{s}}$ with the Extended Lee Weight

TL;DR

This paper studies codes over the ring rac{rac{p^s}{p^s}} with the extended Lee weight, establishing bounds, defining optimal codes, and exploring their algebraic properties and Gray images.

Contribution

It introduces Singleton bounds for these codes, defines MLDS and MLDR codes, and analyzes their kernels, linearity, and duality properties.

Findings

Established Singleton bounds for codes over rac{rac{p^s}{p^s}} with extended Lee weight

Defined and characterized MLDS and MLDR codes in this setting

Analyzed the kernels, linearity, and duality of Gray images of these codes

Abstract

We consider codes over $\mathbb{Z}_{p^s}$ with the extended Lee weight. We find Singleton bounds with respect to this weight and define MLDS and MLDR codes accordingly. We also consider the kernels of these codes and the notion of independence of vectors in this space. We investigate the linearity and duality of the Gray images of codes over $\mathbb{Z}_{p^s}$.