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

Explicit MDS Codes with Complementary Duals