Structure of codes over the ring


Bayram A., Siap I.

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, vol.24, no.5, pp.369-386, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 5
  • Publication Date: 2013
  • Doi Number: 10.1007/s00200-013-0208-x
  • Title of Journal : APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
  • Page Numbers: pp.369-386

Abstract

In this paper, we study the structure of linear codes over the non chain ring . In order to study the codes, we first study the structure of this ring via a distance preserving Gray map which also induces a relation between codes over this ring and ternary codes. Further, the algebraic structure of cyclic and dual codes is also studied. A MacWilliams type Identity between the Gray weight enumerators of the original code and its dual is established. In all cases examples that illustrate the theorems and lemmas are provided. Also, a BCH-type bound and an example that attains this bound is presented.