Optimal Ternary Cyclic Codes From Monomials
Optimal Ternary Cyclic Codes From Monomials
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DOI：
10.1109/tit.2013.2260795
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发表时间：
2013-04
影响因子：
2.5
通讯作者：
C. Ding;T. Helleseth
中科院分区：
文献类型：
--
作者：
C. Ding;T. Helleseth
循环代码是线性代码的子类，并且在消费电子，数据存储系统和通信系统中具有有效的编码和解码算法。在2005年，采用了完美的非线性单元来构建具有参数[3M-1、3M-1-2M，4]的最佳三元循环代码。 GF（3M）上的单个元素用于构建具有相同参数的最佳三元循环代码。还提出了此类代码上的九个开放问题。
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. Perfect nonlinear monomials were employed to construct optimal ternary cyclic codes with parameters [3m-1, 3m-1-2m, 4] by Carlet, Ding, and Yuan in 2005. In this paper, almost perfect nonlinear monomials, and a number of other monomials over GF(3m) are used to construct optimal ternary cyclic codes with the same parameters. Nine open problems on such codes are also presented.