Applicable Algebra in Engineering Communication and Computing

Construction of new quantum codes derived from constacyclic codes over $${\mathbb {F}}_{q^2}+u{\mathbb {F}}_{q^2}+\cdots +u^{r-1}{\mathbb {F}}_{q^2}$$

Xiaoping Shi, Xinmei Huang, Qin Yue

Published Jan 20, 2020• 9 citations

DOI: 10.1007/s00200-020-00415-1

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Applicable Algebra in Engineering Communication and Computing

Construction of new quantum codes derived from constacyclic codes over ${\mathbb {F}}_{q^2}+u{\mathbb {F}}_{q^2}+\cdots +u^{r-1}{\mathbb {F}}_{q^2}$ Construction of new quantum codes derived from constacyclic codes over $${\mathbb {F}}_{q^2}+u{\mathbb {F}}_{q^2}+\cdots +u^{r-1}{\mathbb {F}}_{q^2}$$

Xiaoping Shi, Xinmei Huang, Qin Yue

Published Jan 20, 2020• 9 citations

Publisher

DOI: 10.1007/s00200-020-00415-1

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Construction of new quantum codes derived from constacyclic codes over

{\mathbb {F}}_{q^2}+u{\mathbb {F}}_{q^2}+\cdots +u^{r-1}{\mathbb {F}}_{q^2}

Constacyclic codes over

\mathbb {F}_{q^{2}} \times (\mathbb {F}_{q^{2}}+v\mathbb {F}_{q^{2}})

and their applications in constructing new quantum codes

Constacyclic codes over the ring

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

F q + v F q + v 2 F q and their applications of constructing new non-binary quantum codes

u-Constacyclic codes over

{\mathbb {F}}_p+u{\mathbb {F}}_p

F p + u F p and their applications of constructing new non-binary quantum codes

Constacyclic codes over

{\pmb {\mathbb {F}}}_{q^2}[u]/\langle u^2-w^2 \rangle

and their application in quantum code construction

New MDS operator quantum error-correcting codes derived from constacyclic codes over

\mathbb {F}_{q^2}+v\mathbb {F}_{q^2}

Constacyclic codes over

\mathbb{F}_q R_r

and new quantum codes