On the Weights of General MDS Codes

The weight spectra of MDS codes of length n and dimension k over arbitrary alphabets are studied. For all q -ary MDS codes of dimension k and length ${n}\ne {q}+{k}-1 $ containing the zero codeword, it is shown that all k weights from n to ${n}-{k}+1 $ are realized. The weight spectrum in 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.