摘要
循环码是一类特殊的线性码,由于循环码快速的编码和译码算法,它被广泛应用于消费电子,数据存储以及通信系统当中.在本文中,利用特征是偶数的有限域上的三项式构造出了两类二元循环码,我们不仅可以确定出这两类循环码最小距离的下界,而且这两类循环码在参数的选取上非常的灵活.
Cyclic codes are a subclass of linear codes and have wide applications in consumer electronics, datastorage systems, and communication systems since they have efficient encoding and decoding algorithms. Inthis paper, some trinomials over finite fields with even characteristic are employed to construct two classws ofbinary cyclic codes. Lower bounds on the minimum weight of some cyclic codes are developed. The dimensionsof the codes obtained in this paper are flexible.
出处
《纯粹数学与应用数学》
2016年第4期380-386,共7页
Pure and Applied Mathematics
基金
国家自然科学基金(11401468
11471178)
关键词
循环码
三项式
序列
有限域
cyclic codes, trinomial, sequences, finite fields
