An r-identifying code on a graph G is a set CβV(G) such that for
every vertex in V(G), the intersection of the radius-r closed neighborhood
with C is nonempty and different. Here, we provide an overview on codes for
the n-dimensional lattice, discussing the case of 1-identifying codes,
constructing a sparse code for the 4-dimensional lattice as well as showing
that for fixed n, the minimum density of an r-identifying code is
Ξ(1/rnβ1).Comment: 10p