Additive skew G-codes over finite fields

Dougherty S., Korban A., Şahinkaya S., Ustun D.

Applicable Algebra in Engineering, Communications and Computing, cilt.34, sa.3, ss.423-442, 2023 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 3
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s00200-021-00515-6
  • Dergi Adı: Applicable Algebra in Engineering, Communications and Computing
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.423-442
  • Anahtar Kelimeler: Additive codes, Self-dual codes, Skew codes
  • Ankara Üniversitesi Adresli: Hayır

Özet

We define additive skew G-codes over finite fields and discuss several dualities attached to these codes. We examine the properties of self-dual skew G-codes and in particular we show that the dual, under any duality, of an additive skew G-code is also an additive skew G-code. Additionally, we propose a matrix construction for additive skew G-codes and use it to construct several examples of extremal self-dual additive skew G-codes over the finite field F4. Such codes have a strong connection to quantum error correcting codes.