Title :
Product Constructions for Perfect Lee Codes
Author_Institution :
Dept. of Comput. Sci., Technion - Israel Inst. of Technol., Haifa, Israel
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.
Keywords :
nonlinear codes; Golomb conjecture; Lee metrics; Manhattan metrics; Welch conjecture; diameter perfect Lee codes; nonlinear diameter perfect codes; Hamming distance; Lattices; Linear code; Anticode; Hamming scheme; Lee metric; Manhattan metric; diameter perfect code; perfect code; periodic code; product construction;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2011.2161133
