Z(2)Z(4)-Additive Cyclic Codes


Abualrub T., Siap I. , Aydin N.

IEEE TRANSACTIONS ON INFORMATION THEORY, vol.60, no.3, pp.1508-1514, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 60 Issue: 3
  • Publication Date: 2014
  • Doi Number: 10.1109/tit.2014.2299791
  • Title of Journal : IEEE TRANSACTIONS ON INFORMATION THEORY
  • Page Numbers: pp.1508-1514

Abstract

In this paper, we study Z(2)Z(4)-additive cyclic codes. These codes are identified as Z(4)[x]-submodules of the ring R-r,R-s = Z(2)[x]/< x(r) - 1 > x Z(4) [x]/< x(s)-1 >. The algebraic structure of this family of codes is studied and a set of generator polynomials for this family as a Z(4)[x]-submodule of the ring R-r,R-s is determined. We show that the duals of Z(2)Z(4)-additive cyclic codes are also cyclic. We also present an infinite family of Maximum Distance separable with respect to the singleton bound codes. Finally, we obtain a number of binary linear codes with optimal parameters from the Z(2)Z(4)-additive cyclic codes.