Non-binary quantum synchronizable codes based on cyclic codes over $\textrm{F}_q$ Non-binary quantum synchronizable codes based on cyclic codes over $$\textrm{F}_q$$

Shiwen Sun, Tongjiang Yan, Yuhua Sun +2 more

Quantum Information ProcessingJan 19, 20232 citations

Non-Binary Quantum Codes from Cyclic Codes over $\mathbb {F}_{p} \times (\mathbb {F}_{p}+v\mathbb {F}_{p})$ Non-Binary Quantum Codes from Cyclic Codes over $\mathbb {F}_{p} \times (\mathbb {F}_{p}+v\mathbb {F}_{p})$

Fatma Çalışkan, Tülay Yıldırım, Refia Aksoy

International Journal of Theoretical PhysicsFeb 1, 202310 citations

New Binary Quantum Codes Constructed from Quasi-Cyclic Codes

Chaofeng Guan, Ruihu Li, Liangdong Lü +1 more

arXiv:2112.07137International Journal of Theoretical PhysicsJun 1, 202212 citations

Entanglement-assisted binary quantum codes from skew cyclic codes over ${\mathbb {F}}_2 \times ({\mathbb {F}}_2+v{\mathbb {F}}_2)$ Entanglement-assisted binary quantum codes from skew cyclic codes over $${\mathbb {F}}_2 \times ({\mathbb {F}}_2+v{\mathbb {F}}_2)$$

Fatma Çalışkan, Refia Aksoy, Nuh Aydın +1 more

Quantum Information ProcessingMay 10, 20231 citation

Cyclic codes over F2 × (F2 + vF2) and binary quantum codes

Fatma Çalışkan, Refia Aksoy

In the present study, we define cyclic codes over the commutative principal ideal ring F2 ? (F2 + vF2) with v2 = v and obtain some results on cyclic codes over F2 ? (F2 + vF2). We also investigate the dual of a cyclic code over F2 ? (F2 + vF2) depending on two inner products. We determine a generator polynomial of cyclic codes and give the calculation of the number of cyclic codes over F2 ? (F2 + vF2). Furthermore, we show that the Gray images of a cyclic code over F2 ? (F2 + vF2) of length n are binary quasi-cyclic codes of length 3n and of index 3. We find numerous binary codes as Gray images of cyclic codes over F2 ? (F2 + vF2) and tabulate the optimal ones. Moreover, we show that it is possible to obtain binary quantum error-correcting codes (QECCs) from cyclic codes over F2 ? (F2 + vF2).In the present study, we define cyclic codes over the commutative principal ideal ring F2 ? (F2 + vF2) with v2 = v and obtain some results on cyclic codes over F2 ? (F2 + vF2). We also investigate the dual of a cyclic code over F2 ? (F2 + vF2) depending on two inner products. We determine a generator polynomial of cyclic codes and give the calculation of the number of cyclic codes over F2 ? (F2 + vF2). Furthermore, we show that the Gray images of a cyclic code over F2 ? (F2 + vF2) of length n are binary quasi-cyclic codes of length 3n and of index 3. We find numerous binary codes as Gray images of cyclic codes over F2 ? (F2 + vF2) and tabulate the optimal ones. Moreover, we show that it is possible to obtain binary quantum error-correcting codes (QECCs) from cyclic codes over F2 ? (F2 + vF2).

FilomatJan 1, 20231 citation

Quantum Cyclic Codes Over ℤ m ${\mathbb{Z}}_m$ Quantum Cyclic Codes Over ℤ m $$ {\mathbb{Z}}_m $$

Nianqi Tang, Zhuo Li, Lijuan Xing +1 more

International Journal of Theoretical PhysicsFeb 13, 20190 citations

Binary Quantum Codes from Cyclic Codes over

\mathfrak {R}_{s_{1},s_{2}}

Non-binary quantum synchronizable codes based on cyclic codes over

\textrm{F}_q

Non-Binary Quantum Codes from Cyclic Codes over

\mathbb {F}_{p} \times (\mathbb {F}_{p}+v\mathbb {F}_{p})

Entanglement-assisted binary quantum codes from skew cyclic codes over

{\mathbb {F}}_2 \times ({\mathbb {F}}_2+v{\mathbb {F}}_2)

Quantum Cyclic Codes Over ℤ m

{\mathbb{Z}}_m