Three New Classes Of Entanglement-Assisted Quantum MDS Codes From Cyclic Codes

Abstract

In the quantum coding theory, quantum maximum distance separale (MDS) codes that satisfy the quantum Singleton bound have become an important research topic. However, it is not an easy task to find quantum MDS codes with minimum distance more than $q+1$. Entanglement-assisted quantum MDS (EAQMDS) codes form an important family of quantum codes that can improve the minimum distance of quantum MDS codes to exceed $q+1$. Let q be an odd prime power. In this paper, using a formula on the number of maximally entangled states, we construct three classes of EAQMDS codes of length $n=\frac{q^2-1}{\lambda _{1}\lambda _{2}}$, where $\lambda _{1}$ and $\lambda _{2}$ are odd factors of $q-1$ and $q+1$, respectively. Most of these EAQMDS codes are new in the sense that their parameters are not covered by the codes available in the literature. Moreover, the minimum distance of these resulting codes is larger than $q+1$.