Product Constructions for Perfect Lee Codes

Authors:
Tuvi Etzion
Affiliations:
Department of Computer Science, Technion—Israel Institute of Technology, Haifa, Israel
Venue:
IEEE Transactions on Information Theory
Year:
2011

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Abstract

A well-known conjecture of Golomb and Welch is that the only nontrivial perfect codes in the Lee and Manhattan metrics have length two or minimum distance three. This problem and related topics were subject for extensive research in the last 40 years. In this paper, two product constructions for perfect Lee codes and diameter perfect Lee codes are presented. These constructions yield a large number of nonlinear perfect codes and nonlinear diameter perfect codes in the Lee and Manhattan metrics. A short survey and other related problems on perfect codes in the Lee and Manhattan metrics are also discussed.