  We consider the following generalization of an $(n,k)$ MDS code for
application to an erasure channel with additive noise. Like an MDS code, our
code is required to be decodable from any $k$ received symbols, in the absence
of noise. In addition, we require that the noise margin for every allowable
erasure pattern be as large as possible and that the code satisfy a power
constraint. In this paper we derive performance bounds and present a few
designs for low rank lattice codes for an additive noise channel with erasures.
