It is shown that in the infinite square grid the density of every (r,â‰¤ 2)-identifying code is at least 1/8 and that there exists a sequence Cr of (r,â‰¤ 2)-identifying codes such that the density of Crâ€¦ (More)

Assume that G = (V ,E) is an undirected graph, and C âŠ† V . For every v âˆˆ V , denote Ir(G; v) = {u âˆˆ C : d(u, v) â‰¤ r}, where d(u, v) denotes the number of edges on any shortest path from u to v in G.â€¦ (More)

The motivation for identifying codes comes from maintenance of multiprocessor architectures. In this paper, we give infinite families of optimal edge-robust identifying codes and vertex-robustâ€¦ (More)

We consider upper bounds on two fundamental parameters of a code; minimum distance and covering radius. New upper bounds on the covering radius of non-binary linear codes are derived by generalizingâ€¦ (More)

Let G = (V, E) be an undirected graph without loops and multiple edges. A subset C âŠ† V is called identifying if for every vertex x âˆˆ V the intersection of C and the closed neighbourhood of x isâ€¦ (More)