DocumentCode
1263153
Title
Product Constructions for Perfect Lee Codes
Author
Etzion, Tuvi
Author_Institution
Dept. of Comput. Sci., Technion - Israel Inst. of Technol., Haifa, Israel
Volume
57
Issue
11
fYear
2011
Firstpage
7473
Lastpage
7481
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;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/TIT.2011.2161133
Filename
5936731
Link To Document