LAUSR

Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. The paper is devoted to the construction of new quantum MDS codes based on classical constacyclic codes and cyclic codes over Fq2$\mathbb {F}_{q^{2}}$. We construct a family of new quantum MDS codes with length n=q2+1a$n=\frac {q^{2}+ 1}{a}$, which is a generalization of results in Zhang and Ge (IEEE Trans. Inf. Theory 61(9):5224–5228, 2015), Chen et al. (IEEE. Trans. Inf. Theory 61:1474–1484, 2015). Most of these quantum MDS codes are new in the sense that their parameters are not covered by the quantum codes available in the literature.