Quantum Information Processing

Constacyclic codes over $$F_q[u_{1}, u_{2}, \cdots , u_{k}]/\langle u_{i}^3-u_{i},u_{i}u_{j}-u_{j}u_{i}\rangle $$ and their applications of constructing quantum codes

Zhulin Ji, Shunhua Zhang

Published Dec 19, 2022• 1 citation

DOI: 10.1007/s11128-022-03775-4

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Constacyclic codes over

F_q[u_{1}, u_{2}, \cdots , u_{k}]/\langle u_{i}^3-u_{i},u_{i}u_{j}-u_{j}u_{i}\rangle

and their applications of constructing quantum codes

Constacyclic codes over

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

and their application in quantum code construction

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

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 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

{\mathbb {F}}_qR

-linear skew constacyclic codes and their application of constructing quantum codes

Construction of quantum codes from

\lambda

-constacyclic codes over the ring

\frac{\mathbb {F}_p[u,v]}{\langle v^3-v , u^3-u , uv-vu\rangle }