  MDS codes and self-dual codes are important families of classical codes in
coding theory. It is of interest to investigate MDS self-dual codes. The
existence of MDS self-dual codes over finite field $F_q$ is completely solved
for $q$ is even. In this paper, for finite field with odd characteristic, we
construct some new classes of MDS self-dual codes by (extended) generalized
Reed-Solomon codes.
