  The present paper focuses on the construction of a set of submatrices of a
circulant matrix such that it is a smaller set to verify that the circulant
matrix is an MDS (maximum distance separable) one, comparing to the complete
set of square submatrices needed in general case. The general MDS verification
method requires to test for singular submatrices: if at least one square
submatrix is singular the matrix is not MDS. However, the complexity of the
general method dramatically increases for matrices of a greater dimension. We
develop an algorithm that constructs a smaller subset of submatrices thanks to
a simple structure of circulant matrices. The algorithm proposed in the paper
reduces the size of the testing set by approximately two matrix orders.
