Self-dual cyclic and quantum codes over Z(2) X (Z(2)
DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, vol.11, 2019 (ESCI, Scopus)
- 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.