论文标题
一类Constacyclic代码是通用的Reed-Solomon代码
A class of constacyclic codes are generalized Reed-Solomon codes
论文作者
论文摘要
从给定的长度和代码尺寸无法提高最小距离的意义上，最大距离可分离（MDS）代码是最佳的。最突出的MDS代码是通用的Reed-Solomon（GRS）代码。线性代码$ \ MATHCAL {C} $的Square $ \ MATHCAL {C}^{2} $是由$ \ Mathcal {C} $中每对CodeWords的组成产品跨越的线性代码。对于MDS代码$ \ MATHCAL {C} $，通过确定$ \ Mathcal {C}^{2} $的尺寸，确定$ \ Mathcal {C} $是否为GRS代码很方便。在本文中，我们研究了MDS Constacyclic代码为GRS的条件。为此，我们首先研究了constacyclic代码的平方。然后，我们给出了足够的条件，即constacyclic代码为grs。特别是，我们提供了一种必要和充分的条件，即质量长度的constacyclic代码为grs。
Maximum distance separable (MDS) codes are optimal in the sense that the minimum distance cannot be improved for a given length and code size. The most prominent MDS codes are generalized Reed-Solomon (GRS) codes. The square $\mathcal{C}^{2}$ of a linear code $\mathcal{C}$ is the linear code spanned by the component-wise products of every pair of codewords in $\mathcal{C}$. For an MDS code $\mathcal{C}$, it is convenient to determine whether $\mathcal{C}$ is a GRS code by determining the dimension of $\mathcal{C}^{2}$. In this paper, we investigate under what conditions that MDS constacyclic codes are GRS. For this purpose, we first study the square of constacyclic codes. Then, we give a sufficient condition that a constacyclic code is GRS. In particular, We provide a necessary and sufficient condition that a constacyclic code of a prime length is GRS.
