Coding with injections

A permutation code of length n and minimum distance d is a set Γ of permutations from some fixed set of n symbols such that the Hamming distance between any distinct ${u,v \in \Gamma}$ is at least d. As a generalization, we introduce the problem of packing injections from an m-set, m ≤?n, sometimes called m-arrangements, relative to Hamming distance. We offer some preliminary coding-theoretic bounds, a few design-theoretic connections, and a short discussion on possible applications.