  This paper has two goals. The first one is to discuss good codes for packing
problems in the Lee and Manhattan metrics. The second one is to consider
weighing matrices for some of these coding problems. Weighing matrices were
considered as building blocks for codes in the Hamming metric in various
constructions. In this paper we will consider mainly two types of weighing
matrices, namely conference matrices and Hadamard matrices, to construct codes
in the Lee (and Manhattan) metric. We will show that these matrices have some
desirable properties when considered as generator matrices for codes in these
metrics. Two related packing problems will be considered. The first is to find
good codes for error-correction (i.e. dense packings of Lee spheres). The
second is to transform the space in a way that volumes are preserved and each
Lee sphere (or conscribed cross-polytope), in the space, will be transformed to
a shape inscribed in a small cube.
