  In 1964, Massey introduced a class of codes with complementary duals which
are called Linear Complimentary Dual (LCD for short) codes. He showed that LCD
codes have applications in communication system, side-channel attack (SCA) and
so on. LCD codes have been extensively studied in literature. On the other
hand, MDS codes form an optimal family of classical codes which have wide
applications in both theory and practice. The main purpose of this paper is to
give an explicit construction of several classes of LCD MDS codes, using tools
from algebraic function fields. We exemplify this construction and obtain
several classes of explicit LCD MDS codes for the odd characteristic case.
