On the Covering Radius of Some Modular Codes

TL;DR

This paper investigates the covering radius of certain modular codes over rac{Z}{2^s} with respect to homogeneous distance, providing bounds and exact values for specific code families.

Contribution

It establishes bounds and exact covering radii for Repetition, Simplex, and MacDonald codes over rac{Z}{2^s}, advancing understanding of their geometric properties.

Findings

Exact covering radius for Repetition and Simplex codes

Bounds on MacDonald codes over rac{Z}{4}

New insights into code covering properties

Abstract

This paper gives lower and upper bounds on the covering radius of codes over $\Z_{2^s}$ with respect to homogenous distance. We also determine the covering radius of various Repetition codes, Simplex codes (Type $\alpha$ and Type $\beta$) and their dual and give bounds on the covering radii for MacDonald codes of both types over $\Z_4$.