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- Title
Quantum codes from codes over the ring Fq+αFq.
- Authors
Güzeltepe, Murat; Sarı, Mustafa
- Abstract
In this paper, we aim to obtain quantum error correcting codes from codes over a nonlocal ring R q = F q + α F q . We first define a Gray map φ from R q n to F q 2 n preserving the Hermitian orthogonality in R q n to both the Euclidean and trace-symplectic orthogonality in F q 2 n . 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 φ , we obtain two classes of q-ary quantum codes. We also determine the structure of additive cyclic codes over R p 2 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 δ , we construct a family of p-ary quantum codes.
- Subjects
ERROR-correcting codes; QUANTUM error correcting codes; CYCLIC codes; QUANTUM rings
- Publication
Quantum Information Processing, 2019, Vol 18, Issue 12, pN.PAG
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-019-2476-2