Perfect codes in Doob graphs

被引：9
|
作者：
Krotov, Denis S. [1 ,2 ]
机构：
[1] Sobolev Inst Math, Novosibirsk 630090, Russia
[2] Novosibirsk State Univ, Novosibirsk 630090, Russia
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2016年 / 80卷 / 01期
基金：
俄罗斯科学基金会;
关键词：
Perfect codes; Doob graphs; Distance regular graphs; ERROR-CORRECTING CODES; JOHNSON SCHEME; CONSTRUCTION; ALPHABETS;
D O I：
10.1007/s10623-015-0066-6
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We study -perfect codes in Doob graphs . We show that such codes that are linear over the Galois ring exist if and only if there exist integers and such that and . We also prove necessary conditions on for -perfect codes that are linear over (we call such codes additive) to exist in graphs; for some of these parameters, we show the existence of codes. For every and satisfying and , we construct -perfect codes in , which do not necessarily have a group structure.
引用
收藏
页码：91 / 102
页数：12
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