New classes of entanglement-assisted quantum MDS codes

In this paper, two new classes of entanglement-assisted quantum MDS codes (EAQMDS codes for short) with length n being a factor of $$q^2\pm 1$$ are presented via cyclic codes over finite fields of odd characteristic. Among our constructions, there are several EAQMDS codes with new parameters which have never been reported. Moreover, some of them have much larger minimum distance than known results.