Dihedral codes with 1-dimensional hulls and 1-dimensional linear complementary pairs of dihedral codes

Dougherty S., Şahinkaya S., Ustun D.

Applicable Algebra in Engineering, Communications and Computing, cilt.36, sa.3, ss.471-491, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 3
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s00200-023-00617-3
  • Dergi Adı: Applicable Algebra in Engineering, Communications and Computing
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.471-491
  • Anahtar Kelimeler: 1-Dimensional hull, Group codes, LCD codes
  • Ankara Üniversitesi Adresli: Hayır

Özet

In this paper, we study dihedral codes with 1-dimensional hulls and we determine precisely when dihedral codes over finite fields with 1-dimensional hulls exist. Moreover, we show that these codes come canonically in pairs. We also introduce 1-dimensional linear complementary pairs of dihedral codes and examine the properties of this class of codes. As an application, we obtain 1-dimensional linear complementary pair of dihedral codes, which are either optimal or near optimal.