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.
翻译：最大距离可分离( MDS) 代码是最佳的, 也就是说, 在给定长度和代码大小上, 最小距离无法改进。 最突出的 MDS 代码是通用 Reed- Solomon 代码。 线性代码的平方$\ mathcal{C\2}$是每对代号的构件产品所覆盖的线性代码 $\ mathcal{C} $。 对于 MDS 代码 $\ mathcal{C} $, 方便地确定$\ mathcal{C} $ 是通用的 GRS 代码。 在本文中, 我们调查在什么条件下, MDS 共序代码是 GRS 。 为此, 我们首先研究共序代码的方形 。 然后, 我们给出一个足够的条件, 共序代码是 GRS 。 特别是, 我们提供了一种必要和充分的条件, 使一个主长的共序代码是 GRS 。
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