Hermitian Rank Metric Codes and Duality

La Cruz, Javier De
Evilla, Jorge Robinson
Özbudak, Ferruh
In this paper we define and study rank metric codes endowed with a Hermitian form. We analyze the duality for F-q2-linear matrix codes in the ambient space (F-q2)(n,m) and for both F-q2-additive codes and F-q2m-linear codes in the ambient space F-q2m(n). Similarly, as in the Euclidean case we establish a relationship between the duality of these families of codes. For this we introduce the concept of q(m)-duality between bases of F-q2m over F-q2 and prove that a q(m)-self dual basis exists if and only if m is an odd integer. We obtain connections on the dual codes in F-q2m(n) and (F-q2)(n,m) with the corresponding inner products. In particular, we study Hermitian linear complementary dual, Hermitian self-dual and Hermitian self-orthogonal codes in F-q2m(n) and (F-q2)(n,m). Furthermore, we present connections between Hermitian F-q2-additive codes and Euclidean F-q2-additive codes in F-q2m(n)
Citation Formats
J. D. La Cruz, J. R. Evilla, and F. Özbudak, “Hermitian Rank Metric Codes and Duality,” pp. 38479–38487, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/89457.