Quantum Codes From Cyclic Codes Over The Ring R2

International Conference on Quantum Science and Applications 2016

Altinel, Alev^1 ; Güzeltepe, Murat^1

Department of Mathematics, Sakarya University, Sakarya

TR54187, Turkey^1

关键词: Cyclic code;    Quantum codes;    Quantum error correcting codes;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/766/1/012022/pdf
DOI  :  10.1088/1742-6596/766/1/012022

来源: IOP

【 摘 要 】

Let R2denotes the ring F2+ μF2+ υ2+ μυF2+ wF2+ μwF2+ υwF2+ μυwF2. In this study, we construct quantum codes from cyclic codes over the ring R2, for arbitrary length n, with the restrictions μ2= 0, υ2= 0, w2= 0, μυ = υμ, μw = wμ, υw = wυ and μ (υw) = (μυ) w. Also, we give a necessary and sufficient condition for cyclic codes over R2that contains its dual. As a final point, we obtain the parameters of quantum error-correcting codes from cyclic codes over R2 and we give an example of quantum error-correcting codes form cyclic codes over R2.