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

Coding for the Lee and Manhattan Metrics with Weighing Matrices