The Existence of Perfect Codes in Doob Graphs

被引：4
|
作者：
Krotov, Denis S. [1 ]
机构：
[1] Sobolev Inst Math, Novosibirsk 630090, Russia
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2020年 / 66卷 / 03期
基金：
俄罗斯科学基金会;
关键词：
Additives; Information theory; Indexes; Information processing; Modulation; Tools; Mathematics; Perfect codes; Doob graphs; Eisenstein-Jacobi integers; DISTANCE-REGULAR COVERINGS; POLYNOMIALS;
D O I：
10.1109/TIT.2019.2946612
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We solve the problem of existence of perfect codes in the Doob graph. It is shown that 1-perfect codes in the Doob graph D(m, n) exist if and only if 6m + 3n + 1 is a power of 2; that is, if the size of a 1-ball divides the number of vertices.
引用
收藏
页码：1423 / 1427
页数：5
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