Quantum codes from cyclic codes over F3 + μF3 + υF3 + μυ F3

International Conference on Quantum Science and Applications 2016

Özen, Mehmet^1 ; Özzaim, N. Tuba^1 ; Ince, Halit^1

Department of Mathematics, Sakarya University, Sakarya, Turkey^1

关键词: Computer search;    Cyclic code;    Decomposition theory;    Generator polynomial;    Gray map;    Quantum codes;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/766/1/012020/pdf
DOI  :  10.1088/1742-6596/766/1/012020

来源: IOP

【 摘 要 】

In this paper, it will be argued that structure of cyclic codes over F3+ μF3+ υF3+ μυ F3where u2= 1, v2= 1 and uv = vu for arbitrary length n. We define a new Gray map which is a distance preserving map. By using decomposition theory, we find generator polynomials of cyclic codes over F3+ μF3+ υF3+ μυ F3and obtain the result that cyclic codes over F3+ μF3+ υF3+ μυ F3are principally generated. Further, using these results we determine the parameters of quantum codes which constructed from cyclic codes over F3+ μF3+ υF3+ μυ F3. We present some of the results of computer search.