Two Families of Entanglement-Assisted Quantum MDS Codes from Cyclic Codes

With entanglement-assisted (EA) formalism, arbitrary classical linear codes are allowed to transform into EAQECCs by using pre-shared entanglement between the sender and the receiver. In this paper, based on classical cyclic MDS codes by exploiting pre-shared maximally entangled states, we construct two families of q-ary entanglement-assisted quantum MDS codes [[q(2)+1 a; q(2)+1 a -2 d-1+c; d]]; chh ii, where q is a prime power in the form of am + l, and a = (l(2) + 1) or a = (l(2) +1)/5. We show that all of q-ary EAQMDS have minimum distance upper limit much larger than the known quantum MDS (QMDS) codes of the same length. Most of these q-ary EAQMDS codes are new in the sense that their parameters are not covered by the codes available in the literature.