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

On Quantum Codes Obtained From Cyclic Codes Over $\F_2+u\F_2+u^2\F_2$

Sukhamoy Pattanayak, Abhay Kumar Singh, Pratyush Kumar

Jan 11, 20160 citations

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

On Quantum Codes Obtained From Cyclic Codes Over $\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$ On Quantum Codes Obtained From Cyclic Codes Over $\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$

Sukhamoy Pattanayak, Abhay Kumar Singh, Pratyush Kumar

Let $R=\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$ be a non-chain finite commutative ring, where $u^3=u$ . In this paper, we mainly study the construction of quantum codes from cyclic codes over $R$ . We obtained self-orthogonal codes over $\mathbb{F}_2$ as gray images of linear and cyclic codes over $R$ . The parameters of quantum codes which are obtained from cyclic code over $R$ are discussed.Let $R=\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$ be a non-chain finite commutative ring, where $u^3=u$. In this paper, we mainly study the construction of quantum codes from cyclic codes over $R$. We obtained self-orthogonal codes over $\mathbb{F}_2$ as gray images of linear and cyclic codes over $R$. The parameters of quantum codes which are obtained from cyclic code over $R$ are discussed.

arXiv:1601.02328Jan 11, 20160 citations

Quantum codes from cyclic codes over $F_q+uF_q+vF_q+uvF_q$ F q + u F q + v F q + u v F qQuantum codes from cyclic codes over $$F_q+uF_q+vF_q+uvF_q$$ F q + u F q + v F q + u v F q

Mohammad Ashraf, Ghulam Mohammad

Quantum Information ProcessingJul 11, 201684 citations

Quantum Codes from Cyclic Codes over

F_2+vF_2

Entanglement-assisted binary quantum codes from skew cyclic codes over

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

On Quantum Codes Obtained From Cyclic Codes Over

\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2

Let

R=\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2

be a non-chain finite commutative ring, where

u^3=u

. In this paper, we mainly study the construction of quantum codes from cyclic codes over

R

. We obtained self-orthogonal codes over

\mathbb{F}_2

as gray images of linear and cyclic codes over

R

. The parameters of quantum codes which are obtained from cyclic code over

R

are discussed.

Quantum codes from cyclic codes over

F_q+uF_q+vF_q+uvF_q

F q + u F q + v F q + u v F q