ON LCD CODES OVER FINITE CHAIN RINGS

DURĞUN Y.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, cilt.57, sa.1, ss.37-50, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 57 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.4134/bkms.b181173
  • Dergi Adı: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.37-50
  • Anahtar Kelimeler: LCD codes, projections of linear codes, finite chain rings, LINEAR CODES, COMPLEMENTARY
  • Çukurova Üniversitesi Adresli: Evet

Özet

Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. LCD cyclic codes have been known as reversible cyclic codes that had applications in data storage. Due to a newly discovered application in cryptography, interest in LCD codes has increased again. Although LCD codes over finite fields have been extensively studied so far, little work has been done on LCD codes over chain rings. In this paper, we are interested in structure of LCD codes over chain rings. We show that LCD codes over chain rings are free codes. We provide some necessary and sufficient conditions for an LCD code C over finite chain rings in terms of projections of linear codes. We also showed the existence of asymptotically good LCD codes over finite chain rings.