I. Introduction
We study the existence and provide a construction of a sparsest and balanced generator matrix of Maximum Distance Separable (MDS) codes. A generator matrix is the sparsest if it contains the least number of nonzero entries among all generator matrices of the same MDS code. A generator matrix is balanced if every column contains approximately the same number of nonzero entries. More specifically, we require that the number of nonzero entries in each column differs from each other by at most one.