Self-dual cyclic and quantum codes over Z(2) X (Z(2)

Aydoğdu İ., Abualrub T.

DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, vol.11, 2019 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11
  • Publication Date: 2019
  • Doi Number: 10.1142/s1793830919500411
  • Journal Name: DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Keywords: Z(2)Z(2)[u]-linear codes, cyclic codes, self-dual codes, quantum codes, CSS
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, we introduce self-dual cyclic codes over the ring Z(2) x (Z(2) + uZ(2) ) = Z(2)Z(2)[u]. We determine the conditions for any Z(2)Z(2)[u]-cycliccode to be self-dual, that is, C = C-perpendicular to. Since the binary image of a self-orthogonal Z(2)Z(2)[u]-linear code is also a self-orthogonal binary linear code, we introduce quantum codes over Z(2)Z(2)[u]. Finally, we present some examples of self-dual cyclic and quantum codes that have good parameters.