AN APPLICATION OF A VIRUS OPTIMIZATION ALGORITHM TO THE PROBLEM OF COMPUTING BINARY SELF-DUAL AND LCD CODES

Korban A., Şahinkaya S., Ustun D.

Advances in Mathematics of Communications, cilt.18, sa.5, ss.1390-1405, 2024 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 5
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3934/amc.2022098
  • Dergi Adı: Advances in Mathematics of Communications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1390-1405
  • Anahtar Kelimeler: binary codes, cyclic codes, dihedral codes, LCD codes, Self-dual codes
  • Ankara Üniversitesi Adresli: Hayır

Özet

In this paper, we employ a virus optimization (VO) algorithm, which is one of the metaheuristic optimization techniques, and a known construction method to compute many new binary [72, 36, 12] self-dual codes and optimal/near-optimal linear complementary dual (LCD) codes. In particular, we obtain 39 Type I and 19 Type II codes of length 72, with parameters in their weight enumerators that were not known in the literature before, and 85 new binary LCD codes that are either optimal or near-optimal. We also present the generator matrix of extended Golay code [24, 12, 8] by a cyclic group matrix ring element.