摘要
常循环码是一类重要的线性码,由于其纠错性能易于分析,因而广泛应用于实践中,同时,利用有限环上常循环码还可以直接构造最优线性码。定义了有限非链环F_p+ uF_p+ vF_p上(1+u+v)-循环码的相关概念,讨论了其生成多项式;引入了一种新的Gray映射?,证明了该环上(1+u+v)-循环码在此Gray映射?下的p元象是一个长为2pn的2-准循环码,并由此构造出了两个最优二元准循环码。
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 ？ 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 F p. And by this way, two optimal binary quasi-cyclic codes are constructed.
出处
《计算机工程与应用》
CSCD
北大核心
2016年第1期110-112,223,共4页
Computer Engineering and Applications
基金
安徽高校省级自然科学基金(No.KJ2013Z276)
合肥学院科研发展重点基金(No.10KY01ZD)
合肥学院重点建设学科基金(No.2014XK08)
安徽高校自然科学研究重点项目(No.KJ2015A226)
安徽高校自然科学研究一般项目(No.KJ2015B1105916)
