On Euclidean, Hermitian and symplectic quasi-cyclic complementary dual codes

Linear complementary dual codes (LCD) are codes that intersect trivially with its dual. LCD codes have recently become a popular topic due to their applications in data storage, communication systems, and cryptography. In this paper, we propose a new characterization for LCD codes, which allows us to judge the complementary duality of linear codes from the codeword level. Further, we determine the necessary and sufficient conditions for quasi-cyclic codes to be LCD codes involving Euclidean, Hermitian, and symplectic inner products. Finally, we give several examples demonstrating that quasi-cyclic codes can be utilized to construct good Euclidean, Hermitian, and symplectic LCD codes.