  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.
