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.

翻译：Shi等人[Additive complementary dual codes over F4. Designs, Codes and Cryptography, 2022.]研究了有限域F4上关于迹埃尔米特内积和迹欧几里得内积的加法码。本文定义有限域Fq2上的长度为n的加法码为Fq2^n的加法子群，其中q为素数幂。我们将加法码与称为生成矩阵的矩阵相关联。我们基于有限域Fq2上的生成矩阵刻画了迹欧几里得ACD码和迹埃尔米特ACD码。此外，我们通过Fq上的线性LCD码在Fq2上构造了这些码。