Product Constructions for Perfect Lee Codes
Product Constructions for Perfect Lee Codes
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DOI：
10.1109/tit.2011.2161133
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发表时间：
2011-03
影响因子：
2.5
通讯作者：
T. Etzion
中科院分区：
文献类型：
--
作者：
T. Etzion
Golomb和Welch的一个著名猜想是Lee和曼哈顿度量中唯一的非平凡完美码长度为2或最小距离为3。在过去的40年里，这个问题和相关主题得到了广泛的研究。本文给出了完全Lee码和直径完全Lee码的两种乘积结构。这些构造在Lee和曼哈顿度量中产生了大量的非线性完美码和非线性直径完美码。对Lee和曼哈顿度量中的完美码作了简要的综述，并讨论了其它相关问题。
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.