Integer codes and lattice packings by cubes of sidelength k

Abstract

Integer codes correcting a single error in the maximum metric are considered. This corresponds to a packing of tori by cubes. For an asymmetric error of size one these cubes have side length 2 and the problem can be shown to be equivalent to finding zero-error codes for cycles in the sense of Shannon and Lovasz. For side length greater 3 the equivalence of single error correcting integer codes and zero-error codes does not hold any more.