Non-isomorphic projective MDS codes of dimension two over the Galois field of order 32

The aim of this paper is to classify projective MDS [n,k]_q-codes over the Galois field of order 32 for 4≤n≤17. The proof’s technique which is used was extending (puncturing) the generator matrix by adding columns to the right side of the generator matrix such that any two columns are linearly independent. The dual codes of all such codes are considered and the parity-check matrix of the dual codes are constructed. Finally, the covering radius and weight distribution are founded.