On Quantum Codes Obtained From Cyclic Codes Over F_2+vF_2+v^2F_2
Abdullah Dertli, Yasemin Cengellenmis, Senol Eren
TL;DR
This paper introduces a new Gray map for a specific finite ring and constructs quantum error-correcting codes from cyclic codes over this ring, detailing their parameters and properties.
Contribution
It presents a novel Gray map that preserves weights and distances, and a method to construct quantum codes from cyclic codes over a finite ring.
Findings
A new Gray map is defined for the ring R=F_2+vF_2+v^2F_2.
Quantum codes are constructed from cyclic codes over R.
Parameters of the resulting quantum codes are explicitly determined.
Abstract
A new Gray map which is both an isometry and a weight preserving map from R=F_2+vF_2+v^2F_2 to (F_2)^3 is defined. A construction for quantum error correcting codes from cyclic codes over finite ring R=F_2+vF_2+v^2F_2, v^3=v is given. The parameters of quantum codes which are obtained from cyclic codes over R are determined.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Coding theory and cryptography · Quantum-Dot Cellular Automata