A class of constacyclic codes are generalized Reed-Solomon codes

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 C-2 of a linear code C is the linear code spanned by the component-wise products of every pair of codewords in C. For an MDS code C, it is convenient to determine whether C is a GRS code by determining the dimension of 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.