New singly and doubly even binary [72,36,12] self-dual codes from M2(R)G - group matrix rings

Creative Commons License

Korban A., Şahinkaya S., Ustun D.

Finite Fields and their Applications, cilt.76, 2021 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 76
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1016/j.ffa.2021.101924
  • Dergi Adı: Finite Fields and their Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, MathSciNet, zbMATH
  • Anahtar Kelimeler: Group matrix rings, Self-dual codes
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Ankara Üniversitesi Adresli: Hayır

Özet

In this work, we present a number of generator matrices of the form [I2n|τ2(v)], where I2n is the 2n×2n identity matrix, v is an element in the group matrix ring M2(R)G and where R is a finite commutative Frobenius ring and G is a finite group of order 18. We employ these generator matrices and search for binary [72,36,12] self-dual codes directly over the finite field F2. As a result, we find 134 Type I and 1 Type II codes of this length, with parameters in their weight enumerators that were not known in the literature before. We tabulate all of our findings.