Additive cyclic codes over finite commutative chain rings

Creative Commons License

Martinez-Moro E., Otal K., ÖZBUDAK F.

DISCRETE MATHEMATICS, cilt.341, sa.7, ss.1873-1884, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 341 Sayı: 7
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.disc.2018.03.016
  • Dergi Adı: DISCRETE MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1873-1884
  • Anahtar Kelimeler: Cyclic codes, Additive codes, Codes over rings, Finite commutative chain rings, Galois rings, MULTIVARIABLE CODES, GALOIS RINGS, CONSTRUCTION, PREPARATA, KERDOCK
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

Additive cyclic codes over Galois rings were investigated in Cao et al. (2015). In this paper, we investigate the same problem but over a more general ring family, finite commutative chain rings. When we focus on non-Galois finite commutative chain rings, we observe two different kinds of additivity. One of them is a natural generalization of the study in Cao et al. (2015), whereas the other one has some unusual properties especially while constructing dual codes. We interpret the reasons of such properties and illustrate our results giving concrete examples. (C) 2018 Elsevier B.V. All rights reserved.