On the Construction of Skew Quasi-Cyclic Codes
On the Construction of Skew Quasi-Cyclic Codes
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DOI：
10.1109/tit.2010.2044062
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发表时间：
2010-05-01
影响因子：
2.5
通讯作者：
Siap, Irfan
中科院分区：
文献类型：
--
作者：
Abualrub, Taher;Ghrayeb, Ali;Siap, Irfan
在本文中，我们研究一种称为偏斜QC代码的特殊类型的准循环（QC）代码。这组代码是使用称为偏斜多项式环F [x; theta]。在简要描述了偏斜多项式环F [x； theta]，显示偏斜QC代码是环r（s）（l）=（f [x; theta]/（x（s） - 1））（l）的子模块的子模块。给出了发电机和奇偶校验检查多项式的概念。我们还引入了环F [x; theta]并表明，偏斜QC代码的平价检查多项式是独特的。我们的搜索结果导致构建几个新代码，其锤距距离超过了具有可比参数的先前最著名的线性代码的锤距距离。
In this paper, we study a special type of quasi-cyclic (QC) codes called skew QC codes. This set of codes is constructed using a noncommutative ring called the skew polynomial ring F[x; theta]. After a brief description of the skew polynomial ring F[x; theta], it is shown that skew QC codes are left submodules of the ring R(s)(l) = (F[x; theta]/(x(s) - 1))(l). The notions of generator and parity-check polynomials are given. We also introduce the notion of similar polynomials in the ring F[x; theta] and show that parity-check polynomials for skew QC codes are unique up to similarity. Our search results lead to the construction of several new codes with Hamming distances exceeding the Hamming distances of the previously best known linear codes with comparable parameters.