Cyclic Codes from Some Monomials and Trinomials
Cyclic Codes from Some Monomials and Trinomials
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DOI：
10.1137/120882275
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发表时间：
2013-11
期刊：
影响因子：
--
通讯作者：
C. Ding
中科院分区：
文献类型：
--
作者：
C. Ding
循环码是线性码的子类，并且由于它们具有有效的编码和解码算法而在消费电子、数据存储系统和通信系统中具有应用。本文利用有限域上的一些单项式和三项式构造了一些循环码族。给出了某些循环码族的最小重量的下界。确定了本文所构造的其它码族的最小权。代码的尺寸是灵活的。本文中提出的许多码是最优或几乎最优的，因为它们满足线性码的某些界。还提出了单项式和三项式循环码的一些开放性问题。
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, some monomials and trinomials over finite fields are employed to construct a number of families of cyclic codes. Lower bounds on the minimum weight of some families of the cyclic codes are developed. The minimum weights of other families of the codes constructed in this paper are determined. The dimensions of the codes are flexible. Many of the codes presented in this paper are optimal or almost optimal in the sense that they meet some bounds on linear codes. Open problems regarding cyclic codes from monomials and trinomials are also presented.