Codes from the Skew Ring M2(F2)⋊φG

Dougherty S., Sąhinkaya S., Ustun D.

Virtual Conference in Honor of Tariq Rizvi Noncommutative Rings and their Application VII, NCRA 2021, and Virtual Conference on Quadratic forms, rings and codes, QFRC 2021, Virtual, Online, 08 Temmuz 2021, cilt.785, ss.89-105, (Tam Metin Bildiri) identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 785
  • Doi Numarası: 10.1090/conm/785/15778
  • Basıldığı Şehir: Virtual, Online
  • Sayfa Sayıları: ss.89-105
  • Anahtar Kelimeler: G-codes, Optimal codes, Self-dual codes, Skew codes
  • Ankara Üniversitesi Adresli: Hayır

Özet

In this work, we study codes generated by elements in the skew group matrix ring Mk(R) (Formula Presented), where R is a finite commutative Frobenius ring, G is an arbitrary finite group, and (Formula Presented) is a group homomorphism from G to Aut(Mk(R)). We then determine all possible group homomorphisms (Formula Presented): G → Aut(M2(F2)), for the cases where G is a cyclic group and a dihedral group. Finally, by using skew generator matrices we provide examples of binary self-dual codes and also binary linear optimal codes.