Quantum codes over Fp from cyclic codes over Fp[u, v]/〈u2 − 1, v3 − v, uv − vu〉

New non-binary quantum codes from constacyclic codes over <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_q[u,v]/\langle u^{2}-1, v^{2}-v, uv-vu\rangle $\end{document}</tex-math></inline-formula>

“…Moreover, our quantum code [ [16,6,4]] 13 and [ [24,16,3]] 13 satisfies n + 2 − k − 2d = 4. Other new quantum codes have the larger minimum distance than the known quantum codes in [4,5].…”

“…Then we obtain a new quantum code with parameters [[72, 48, 4]] 3 . This quantum code has the larger minimum distance comparing with the known quantum code with parameters [[72, 48, 2]] 3 appeared in [5].…”

“…a d in columns two, three, four and five. 5 have the larger dimension than the known quantum codes in [4,5]. Moreover, our quantum code [ [16,6,4]] 13 and [ [24,16,3]] 13 satisfies n + 2 − k − 2d = 4.…”

“…= {7}, by Theorem 4.9 we get C ⊥ H ⊆ C , and Φ(C ) is a [24,20,4] linear Hermitian dual-containing code over F 5 2 . Then we obtain a new quantum code with parameters [ [24,16,4]] 5 . This quantum code has parameters satisfying n + 2 − k − 2d = 2.…”

“…Motivated by the above study, many coding scholars have been devoted to the study of quantum codes on general finite rings. In [3], Ashraf et al constructed new quantum codes from cyclic codes over F p + vF p with v 2 = v. In [13], Gao gave a construction of quantum codes from cyclic codes over finite non-chain ring F q + vF q + v 2 F q + v 3 F q with v 4 = v. In [4,5], Ashraf et al again obtained new non-binary quantum codes from cyclic codes over F q + uF q + vF q + uvF q with u 2 = u, v 2 = v, uv = vu and F p [u, v]/ u 2 −1, v 3 −v, uv −vu with u 2 = 1, v 3 = v, uv = vu, respectively. In [21], Liu et al obtained good quantum codes from cyclic codes over the finite chain ring F p 2m + uF p 2m , where u 2 = 0.…”