On Hermitian LCD Generalized Gabidulin Codes

In this paper, we study Hermitian linear complementary dual (abbreviated Hermitian LCD) rank metric codes. A class of Hermitian LCD generalized Gabidulin codes are constructed by qm-self-dual bases of 𝔽q2m over 𝔽q2. Moreover, the exact number of qm-self-dual bases of 𝔽q2m over 𝔽q2 is derived. As a consequence, an upper bound and a lower bound of the number of the constructed Hermitian LCD generalized Gabidulin codes are determined.