Hermitian Rank Metric Codes and Duality


La Cruz J. D. , Evilla J. R. , ÖZBUDAK F.

IEEE ACCESS, vol.9, pp.38479-38487, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9
  • Publication Date: 2021
  • Doi Number: 10.1109/access.2021.3064503
  • Title of Journal : IEEE ACCESS
  • Page Numbers: pp.38479-38487

Abstract

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)