The weight spectra of MDS codes of length n and dimension k over the
arbitrary alphabets are studied. For all q-ary MDS codes of dimension k
containing the zero codeword, it is shown that all k weights from n to
nβk+1 are realized. The remaining case n=q+kβ1 is also determined.
Additionally, we prove that all binary MDS codes are equivalent to linear MDS
codes. The proofs are combinatorial, and self contained