In this paper, the uniqueness of the echelon form generator matrix of a linear code is considered. In addition, an algorithm for testing the existence of a Reed-Solomon (RS) code corresponding to a given MDS matrix is presented. These results show that the number of existing MDS matrices and MDS codes far more abundantly than the RS codes, which is the basis for other studies on the MDS matrices and the MDS codes. | On the correspondence between the MDS matrices and the reed solomon codes
