A Generalization of Lee Codes
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.
Cite
@article{arxiv.1210.5863,
title = {A Generalization of Lee Codes},
author = {Carlos Araujo and Italo J. Dejter and Peter Horak},
journal= {arXiv preprint arXiv:1210.5863},
year = {2013}
}
Comments
17 pages, 13 figures; Designs, Codes and Cryptography 2012