Hermitian Rank Metric Codes and Duality

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

IEEE ACCESS, cilt.9, ss.38479-38487, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1109/access.2021.3064503
  • Dergi Adı: IEEE ACCESS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, Directory of Open Access Journals
  • Sayfa Sayıları: ss.38479-38487
  • Anahtar Kelimeler: Rank metric codes, additive rank metric codes, Hermitian rank metric codes, ERROR-CORRECTION, LINEAR CODES, DISTANCE
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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)