Some new families of entanglement-assisted quantum MDS codes derived from negacyclic codes

摘要

Entanglement-assisted quantum error-correcting codes as a generalization of stabilizer quantum error-correcting (QEC) codes can improve the performance of stabilizer QEC codes and can be constructed from arbitrary classical linear codes by relaxing the dual-containing condition and using pre-shared entanglement states between the sender and the receiver. In this paper, we construct some families of entanglement-assisted quantum maximum distance separable codes with parameters [[q(2)-1/a, q(2)-1/a-2(d - 1)+ c, d; c]](q), where q is an odd prime power with the form q = am +/- l, a = l(2) - 1 or a = l(2)-1/2, l is an odd integer, and m is a positive integer. Most of these codes are new in the sense that their parameters are not covered by the codes available in the literature.

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