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arXiv · 1210.5863

A Generalization of Lee Codes

Carlos Araujo·Italo J. Dejter·Peter Horak
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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.

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Carlos Araujo, Italo J. Dejter, Peter Horak. 2013-08-04. A Generalization of Lee Codes. https://arxiv.org/abs/1210.5863

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