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 :
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