Several constructions of LCD MDS codes

Linear complementary dual codes (LCD codes) have been widely studied because of their significant role in data storage and cryptography. Maximum distance separable codes with complimentary duals (LCD MDS codes) have the greatest error correcting ability, and so the construction of LCD MDS codes is a hot topic. By using the generator matrix of linear codes, the existence results of LCD MDS codes are given by Carlet et al. in 2018. Recently, several display constructions of LCD MDS codes are given by scholars via the generalized Reed-Solomoncodes, the algebraic geometry codes, the constacylic codes and so on. In this paper, we will introduce the main methods, results and recent progress of constructing LCD MDS codes.