# Infinity-Norm Permutation Covering Codes from Cyclic Groups

## TL;DR

This paper introduces a new construction for permutation covering codes under the infinity norm, leveraging cyclic groups to determine covering radii and develop efficient algorithms for codeword search.

## Contribution

It presents a novel code construction using cyclic transitive groups, providing exact covering radii and linear-time algorithms for permutation covering codes.

## Key findings

- Exact covering radius for cyclic transitive groups determined
- Linear-time algorithms developed for finding covering codewords
- Bounds established for relabeled cyclic groups under conjugation

## Abstract

We study covering codes of permutations with the $\ell_\infty$-metric. We provide a general code construction, which uses smaller building-block codes. We study cyclic transitive groups as building blocks, determining their exact covering radius, and showing linear-time algorithms for finding a covering codeword. We also bound the covering radius of relabeled cyclic transitive groups under conjugation.