A generalization of Lee codes

Authors:
C. Araujo;I. Dejter;P. Horak
Affiliations:
University of Puerto Rico, Rio Piedras, USA 00936-8377;University of Puerto Rico, Rio Piedras, USA 00936-8377;University of Washington, Tacoma, USA 98402
Venue:
Designs, Codes and Cryptography
Year:
2014

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Abstract

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.