On Hermitian LCD generalized Gabidulin codes

Abstract

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 q^m-self-dual bases of 𝔽_q^2m over 𝔽_q² . Moreover, the exact number of q^m-self-dual bases of 𝔽_q^2m over 𝔽_q² 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.