  The theory of entanglement-assisted quantum error-correcting codes (EAQECCs)
is a generalization of the standard stabilizer quantum error-correcting codes,
which can be possibly constructed from any classical codes by relaxing the
duality condition and utilizing preshared entanglement between the sender and
receiver. In this paper, a new family of EAQECCs is constructed from negacyclic
codes of length $n=\frac{q^2+1}{a}$, where $q$ is an odd prime power,
$a=\frac{m^2+1}{2}$ and $m$ is an odd integer. Some new entanglement-assisted
quantum maximum distance separable (EAQMDS) codes are obtained in the sense
that their parameters are not covered by the previously known ones.
