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

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 = a m ± 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. [ABSTRACT FROM AUTHOR]