文摘
In this work, we further improve the distance of the quantum maximum distance separable (MDS) codes of length \(n=\frac{q^2+1}{10}\). This yields new families of quantum MDS codes. We also construct a family of new quantum MDS codes with parameters \([[\frac{q^2-1}{3}, \frac{q^2-1}{3}-2d+2, d]]_{q}\), where \(q=2^m\), \(2\le d\le \frac{q-1}{3}\) if \(3\mid (q+2)\), and \(2\le d\le \frac{2q-1}{3}\) if \(3\mid (q+1)\). Compared with the known quantum MDS codes, these quantum MDS codes have much larger minimum distance.