Quantum Codes from Cyclic Codes over the Ring $$R = \mathbbm {F}_{q} + u\mathbbm {F}_{q} + v\mathbbm {F}_{q} +uv \mathbbm {F}_{q} + v^{2}\mathbbm {F}_{q}+ uv^{2}\mathbbm {F}_{q}$$

Mohammed Sabiri, Bassou Aouijil

Lecture notes in networks and systemsJan 1, 20240 citations

Journal of Applied Mathematics and Computing

On quantum and LCD codes from the cyclic codes over the ring $\mathbb {F}_q[\textsf{u}, \textsf{v},\textsf{w}]/\langle \textsf{u}^3-\textsf{u},\textsf{v}^2-\textsf{v}, \textsf{w}^2-\textsf{w}, \textsf{u}\textsf{v}, \textsf{v}\textsf{u}, \textsf{u}\textsf{w}, \textsf{w}\textsf{u}, \textsf{v}\textsf{w}-\textsf{w}\textsf{v} \rangle$ On quantum and LCD codes from the cyclic codes over the ring $$\mathbb {F}_q[\textsf{u}, \textsf{v},\textsf{w}]/\langle \textsf{u}^3-\textsf{u},\textsf{v}^2-\textsf{v}, \textsf{w}^2-\textsf{w}, \textsf{u}\textsf{v}, \textsf{v}\textsf{u}, \textsf{u}\textsf{w}, \textsf{w}\textsf{u}, \textsf{v}\textsf{w}-\textsf{w}\textsf{v} \rangle $$

Pradeep Rai, Bhupendra Singh, Ashok Ji Gupta

Published Feb 17, 2024• 5 citations

Publisher

DOI: 10.1007/s12190-024-02002-w

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{\mathcal{R}}_{7}=\mathbb{F}_{q}+u \mathbb{F}_{q}+

v \mathbb{F}_{q}+w \mathbb{F}_{q}+z \mathbb{F}_{q}+u^{2} \mathbb{F}_{q}+w z \mathbb{F}_{q}

. Through this work we seek to construct new quantum codes and LCD codes by means of cyclic codes built on the ring

{\mathcal{R}}_{7}

. By using cyclic codes containing their duals, we give quantum codes, we also give a method for the construction of LCD Codes over

{\mathcal{R}}_{7}