  Shi et al. [Additive complementary dual codes over F4. Designs, Codes and
Cryptography, 2022.] studied additive codes over the finite field F4 with
respect to trace Hermitian and trace Euclidean inner products. In this article,
we define additive codes of length n over finite field Fq2 as additive
subgroups of Fn q2 where q is a prime power. We associate an additive code with
a matrix called a generator matrix. We characterize trace Euclidean ACD and
trace Hermitian ACD codes in terms of generator matrices over the finite field
Fq2 . Also, we construct these codes over Fq2 from linear LCD codes over Fq.
