Applicable Algebra in Engineering Communication and Computing

Quantum codes from cyclic codes over the ring $${\mathbb {F}}_q+v_1{\mathbb {F}}_q+\cdots +v_r{\mathbb {F}}_q$$ F q + v 1 F q + ⋯ + v r F q

Yun Gao, Jian Gao, Fang‐Wei Fu

Published Jul 21, 2018• 58 citations

DOI: 10.1007/s00200-018-0366-y

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Applicable Algebra in Engineering Communication and Computing

Quantum codes from cyclic codes over the ring ${\mathbb {F}}_q+v_1{\mathbb {F}}_q+\cdots +v_r{\mathbb {F}}_q$ F q + v 1 F q + ⋯ + v r F qQuantum codes from cyclic codes over the ring $${\mathbb {F}}_q+v_1{\mathbb {F}}_q+\cdots +v_r{\mathbb {F}}_q$$ F q + v 1 F q + ⋯ + v r F q

Yun Gao, Jian Gao, Fang‐Wei Fu

Published Jul 21, 2018• 58 citations

Publisher

DOI: 10.1007/s00200-018-0366-y

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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

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Quantum codes from cyclic codes over 𝔽q+v𝔽q+v2𝔽q+v3𝔽q

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Quantum codes from cyclic codes over the ring

{\mathbb {F}}_q+v_1{\mathbb {F}}_q+\cdots +v_r{\mathbb {F}}_q

F q + v 1 F q + ⋯ + v r F q

We give a construction of quantum codes over

{\mathbb{F}_q}

from cyclic codes over a finite non-chain ring

{\mathbb{F}_q} + v{\mathbb{F}_q} + {v^2}{\mathbb{F}_q} + {v^3}{\mathbb{F}_q} + {v^4}{\mathbb{F}_q}

, where q=pr, p is an odd prime, 4|p−1 and v5=v.

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