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 equivalence definition 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.