NEW ENTANGLEMENT-ASSISTED QUANTUM MDS CODES DERIVED FROM CYCLIC CODES

摘要

Entanglement-assisted quantum error-correcting codes, which can be seen as a generalization of quantum error-correcting codes, can be constructed from arbitrary classical linear codes by relaxing the self-orthogonality properties and using pre-shared entangled states between the sender and the receiver, and can also improve the performance of quantum error-correcting codes. In this paper, we construct some families of entanglement-assisted quantum maximum-distance-separable codes with parameters [[ q(2)-1/alpha, q(2) -1/alpha 2d + 2 + c; d; c]](q), where q is a prime power with the form q = am +/- l alpha = l(2)-1/3 is an odd integer, l equivalent to 2 ( mod 6) or l equivalent to 4 ( mod 6), 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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