  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
$ n-k+1 $ are realized. The remaining case $ n=q+k-1 $ is also determined.
Additionally, we prove that all binary MDS codes are equivalent to linear MDS
codes. The proofs are combinatorial, and self contained.
