An important family of quantum codes is the quantum maximum-distance-separable (MDS) codes. In this paper, we construct some new classes of quantum MDS codes by generalized Reed-Solomon (GRS) codes and Hermitian construction. In addition, the length $n$ of most of the quantum MDS codes we constructed satisfies $n\equiv 0,1($ mod $\,\frac{q\pm1}{2})$ , which is different from previously known code lengths. At the same time, the quantum MDS codes we construct have large minimum distances that are greater than $q/2+1$ .An important family of quantum codes is the quantum maximum-distance-separable (MDS) codes. In this paper, we construct some new classes of quantum MDS codes by generalized Reed-Solomon (GRS) codes and Hermitian construction. In addition, the length $n$ of most of the quantum MDS codes we constructed satisfies $n\equiv 0,1($mod$\,\frac{q\pm1}{2})$, which is different from previously known code lengths. At the same time, the quantum MDS codes we construct have large minimum distances that are greater than $q/2+1$.

arXiv:2310.00214Sep 30, 20230 citations

Construction of some new quantum MDS codes

Xueying Shi, Qin Yue, Xiaomeng Zhu

Finite Fields and Their ApplicationsMay 23, 201761 citations

Quantum MDS Codes with length

n\equiv 0,1(

mod

\,\frac{q\pm1}{2})

n

of most of the quantum MDS codes we constructed satisfies

n\equiv 0,1(

mod

\,\frac{q\pm1}{2})

, which is different from previously known code lengths. At the same time, the quantum MDS codes we construct have large minimum distances that are greater than

q/2+1