  Motivated by a problem in computer architecture we introduce a notion of the
perfect distance-dominating set, PDDS, in a graph. PDDSs constitute a
generalization of perfect Lee codes, diameter perfect codes, as well as other
codes and dominating sets. In this paper we initiate a systematic study of
PDDSs. PDDSs related to the application will be constructed and the
non-existence of some PDDSs will be shown. In addition, an extension of the
long-standing Golomb-Welch conjecture, in terms of PDDS, will be stated. We
note that all constructed PDDSs are lattice-like which is a very important
feature from the practical point of view as in this case decoding algorithms
tend to be much simpler.
