计算机工程与应用2016，Vol.52Issue(1)：110-112,223,4.DOI:10.3778/j.issn.1002-8331.1503-0193
环Fp+uFp+vFp上的(1+u+v)-循环码
(1+u+v)- cyclic codes over Fp+uFp+vFp
摘要
Abstract
Constacyclic codes are an important class of linear codes in coding theory. This class of codes has been widely used in practice because its error-correcting performance is easy to be analyzed. Meanwhile, many optimal linear codes are produced directly from constacyclic codes over finite rings. Firstly, the concept of (1+u+v)- cyclic code over Fp+uFp+vFp is defined, and the generator polynomial of (1+u+v)-cyclic codes is discussed. Then, a new Gray map φ from Fp+uFp+ vFp to F 2pp is introduced. It is proved that the Gray image of a (1+u+v)-cyclic code of length n over Fp+uFp+vFp is a linear quasi-cyclic code of index 2 and of length 2pn over Fp . And by this way, two optimal binary quasi-cyclic codes are constructed.关键词
(1+u+v)-循环码/Gray映射/准循环码Key words
(1+u+v)-cyclic code/Gray map/quasi-cyclic code分类
信息技术与安全科学引用本文复制引用
余海峰,张霞..环Fp+uFp+vFp上的(1+u+v)-循环码[J].计算机工程与应用,2016,52(1):110-112,223,4.基金项目
安徽高校省级自然科学基金(No.KJ2013Z276) （No.KJ2013Z276）
合肥学院科研发展重点基金(No.10KY01ZD) （No.10KY01ZD）
合肥学院重点建设学科基金(No.2014XK08) （No.2014XK08）
安徽高校自然科学研究重点项目(No.KJ2015A226) （No.KJ2015A226）
安徽高校自然科学研究一般项目(No.KJ2015B1105916). （No.KJ2015B1105916）
