On the covering radius of Z4-codes and their lattices

In this correspondence, we investigate the covering radius of codes over Z₄ for the Lee and Euclidean distances in relation with those of binary nonlinear codes and lattices obtained by the Gray map and Construction A₄, respectively. We give several upper and lower bounds on covering radii, including Z₄-analogs of the sphere-covering bound, the packing radius bound, the Delsarte bound, and the redundancy bound. We show that any Euclidean-optimal Type II code of length 24 has covering radius 8 with respect to the Euclidean distance. We determine the covering radius of the Klemm codes with respect to the Lee distance. We derive lower bounds on the covering radii of the Niemeier lattices