Skew Constacyclic Codes over a Non-Chain Ring

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KÖROĞLU M. E., SARI M.

Entropy, cilt.25, sa.3, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 3
  • Basım Tarihi: 2023
  • Doi Numarası: 10.3390/e25030525
  • Dergi Adı: Entropy
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: entanglement-assisted quantum codes, LCD codes, non-chain ring, skew constacyclic codes
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we investigate the algebraic structure of the non-local ring (Formula presented.) and identify the automorphisms of this ring to study the algebraic structure of the skew constacyclic codes and their duals over this ring. Furthermore, we give a necessary and sufficient condition for the skew constacyclic codes over (Formula presented.) to be linear complementary dual (LCD). We present some examples of Euclidean LCD codes over (Formula presented.) and tabulate the parameters of Euclidean LCD codes over finite fields as the (Formula presented.) -images of these codes over (Formula presented.), which are almost maximum distance separable (MDS) and near MDS. Eventually, by making use of Hermitian linear complementary duals of skew constacyclic codes over (Formula presented.) and the map (Formula presented.), we give a class of entanglement-assisted quantum error correcting codes (EAQECCs) with maximal entanglement and tabulate parameters of some EAQECCs with maximal entanglement over finite fields.