Product Constructions for Perfect Lee Codes

Details Product Constructions for Perfect Lee Codes Product Constructions for Perfect Lee Codes

2011-03-21

arxiv.org/abs/1103.3933v2

Computer Science

Information Theory

submitted to IEEE Transactions on Information Theory

Scientific paper

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 forty 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 the Manhattan metrics are also discussed.

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