In this correspondence, we investigate the covering radius of codes over Z/sub 4/ for the Lee and Euclidean distances in relation with those of binary nonlinear codes and lattices obtained by the Gray map and Construction A/sub 4/, respectively. We give several upper and lower bounds on covering radii, including Z/sub 4/-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.
展开▼
机译：在此对应关系中，我们研究了Lee / Euclidean距离在Z / sub 4 /上的代码的覆盖半径与分别由格雷图和Construction A / sub 4 /获得的二进制非线性代码和晶格的覆盖半径有关。我们给出了覆盖半径的上下边界，包括球面覆盖边界，填充半径边界，Delsarte边界和冗余边界的Z / sub 4 /模拟。我们表明，长度为24的任何欧几里德最优II类代码都具有相对于欧几里德距离的覆盖半径8。我们确定相对于李距离的克莱姆码的覆盖半径。我们得出涅梅尔晶格的覆盖半径的下界。
展开▼
