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New entanglement-assisted MDS quantum constacyclic codes
(pp766-799)
Hangyu Liu, Sujuan Huang, Liqi Wang, and Shixin Zhu
doi:
https://doi.org/10.26421/QIC24.9-10-4
Abstracts:
Entanglement-assisted quantum
error-correcting codes can be seen as a new-type of quantum
error-correcting codes and can be constructed from arbitrary linear
codes which should not satisfy the dual-containing condition by
utilizing shared entangled states between the sender and the receiver in
advance. In this paper, we construct several new classes of
entanglement-assisted quantum maximum-distance-separable codes from
constacyclic codes and cyclic codes
by exploiting small
pre-shared
entangled states, respectively. These codes are new in the sense that
they are not covered by the codes available in the literature.
Key Words:
Entanglement-assisted quantum
error-correcting codes,
Constacyclic
codes,
Cyclotomic
coset,
MDS
codes |
