Construction of Additive Complementary Dual Codes Over Finite Fields

In this work, we investigate additive complementary dual (ACD) codes and their construction over finite fields ${\mathbb{F}}_{q^2}$ with respect to the trace inner products, where $q$ is a prime power. First, we associate an additive code with a matrix known as a generator matrix. After that, we describe ACD codes in terms of generator matrices for the trace Hermitian and the trace Euclidean inner products. We also construct ACD codes over ${\mathbb{F}}_{q^2}$ from linear codes over ${\mathbb{F}}_q\mathrm{.}$ Additionally, we present techniques for constructing ACD codes with various parameters from a given ACD code over ${\mathbb{F}}_{q^2}\mathrm{.}$ By applying these methods, we construct numbers of trace Euclidean and trace Hermitian ACD codes that exhibit better parameters compared to the best known linear codes over ${\mathbb{F}}_9$ and ${\mathbb{F}}_4$ of the same size and length.