  Linear complementary dual codes (LCD) intersect trivially with their dual. In
this paper, we develop 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 sufficient and necessary conditions for one-generator
quasi-cyclic codes to be LCD codes involving Euclidean, Hermitian, and
symplectic inner products. Finally, we constructed many Euclidean, Hermitian
and symmetric LCD codes with excellent parameters, some improving the results
in the literature. Remarkably, we construct a symplectic LCD $[28,6]_2$ code
with symplectic distance $10$, which corresponds to an trace Hermitian additive
complementary dual $(14,3,10)_4$ code that outperforms the optimal quaternary
Hermitian LCD $[14,3,9]_4$ code.
