Two families of Entanglement-assisted Quantum MDS Codes from cyclic Codes
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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;c]], 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.
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