Infinity-Norm Permutation Covering Codes From Cyclic Groups

We study covering codes of permutations with the $\ell _\infty $ -metric. We provide a general code construction, which combines short building-block codes into a single long code. We focus on cyclic transitive groups as building blocks, determining their exact covering radius, and showing a linear-time algorithm for finding a covering codeword. When used in the general construction, we show that the resulting covering code asymptotically …