A generalization of Lee codes

作者：Araujo C; Dejter I^*; Horak P

来源：Designs, Codes and Cryptography, 2014, 70(1-2): 77-90.

DOI：10.1007/s10623-012-9666-6

• Error-correcting codes
• Distance dominating sets
• Lee metric
• Lattice tiling

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.

• 出版日期2014-1