Nonexistence of perfect 2-error-correcting Lee codes in certain dimensions

被引：19
|
作者：
Kim, Dongryul [1 ]
机构：
[1] Harvard Univ, Cambridge, MA 02138 USA
来源：
EUROPEAN JOURNAL OF COMBINATORICS | 2017年 / 63卷
关键词：
THEOREMS; TILINGS;
D O I：
10.1016/j.ejc.2017.01.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Golomb-Welch conjecture states that there are no perfect e-error-correcting codes in Z(n) for n >= 3 and e >= 2. In this note, we prove the nonexistence of perfect 2-error-correcting codes for a certain class of n, which is expected to be infinite. This result further substantiates the Golomb-Welch conjecture. (C) 2017 Elsevier Ltd. All rights reserved.
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页码：1 / 5
页数：5
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