Quantum codes from codes over the ring F-q + alpha F-q

GÜZELTEPE M., SARI M.

QUANTUM INFORMATION PROCESSING, vol.18, no.12, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 12
  • Publication Date: 2019
  • Doi Number: 10.1007/s11128-019-2476-2
  • Journal Name: QUANTUM INFORMATION PROCESSING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Quantum codes, Cyclic codes, Gray map, ERROR-CORRECTION
  • Yıldız Technical University Affiliated: No

Abstract

In this paper, we aim to obtain quantum error correcting codes from codes over a non-local ring R-q = F-q + alpha F-q. We first define a Gray map phi from R-q(n) to F-q(2n) preserving the Hermitian orthogonality in R-q(n) to both the Euclidean and trace-symplectic orthogonality in F-q(2n). We characterize the structure of cyclic codes and their duals over R-q and derive the condition of existence for cyclic codes containing their duals over R-q. By making use of the Gray map phi, we obtain two classes of q-ary quantum codes. We also determine the structure of additive cyclic codes over R-p2 and give a condition for these codes to be self-orthogonal with respect to Hermitian inner product. By defining and making use of a new map delta, we construct a family of p-ary quantum codes.