On Codes over Local Frobenius Non-Chain Rings of Order 16

被引：26
|
作者：
Martinez-Moro, Edgar [1 ,2 ]
Szabo, Steve [2 ]
机构：
[1] Univ Valladolid, E-47002 Valladolid, Spain
[2] Eastern Kentucky Univ, Richmond, KY USA
来源：
NONCOMMUTATIVE RINGS AND THEIR APPLICATIONS | 2015年 / 634卷
关键词：
NEGACYCLIC CODES; FINITE RINGS;
D O I：
10.1090/conm/634/12702
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Codes over rings is still an emerging area in coding theory. Most of the work done so far has been done on alphabets that are chain rings. As the next logical step in the development of codes over rings, some studies have been done on codes over local Frobenius rings that are not chain rings. In this work, the smallest local Frobenius rings are shown to be of order 16 and a complete list of these seven rings is given. Along the way, all local rings of order 16 are found. In addition to these rings, some commonalities, pertaining to codes, between the local Frobenius non-chain rings are shown.
引用
收藏
页码：227 / 241
页数：15
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