Additive cyclic codes over finite commutative chain rings

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Martinez-Moro E., Otal K., ÖZBUDAK F.

DISCRETE MATHEMATICS, vol.341, no.7, pp.1873-1884, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 341 Issue: 7
  • Publication Date: 2018
  • Doi Number: 10.1016/j.disc.2018.03.016
  • Journal Name: DISCRETE MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1873-1884
  • Keywords: Cyclic codes, Additive codes, Codes over rings, Finite commutative chain rings, Galois rings, MULTIVARIABLE CODES, GALOIS RINGS, CONSTRUCTION, PREPARATA, KERDOCK
  • Middle East Technical University Affiliated: Yes

Abstract

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.