Infinity-Norm Permutation Covering Codes from Cyclic Groups

We study covering codes of permutations with the ${\mathrm{\ell }}_{\mathrm{\infty }}$-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.