Entanglement-assisted quantum MDS codes from constacyclic codes with large minimum distance
Abstract
The entanglement-assisted (EA) formalism allows arbitrary classical linear codes to transform into entanglement-assisted quantum error correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this work, we propose a decomposition of the defining set of constacyclic codes. Using this method, we construct four classes of -ary entanglement-assisted quantum MDS (EAQMDS) codes based on classical constacyclic MDS codes by exploiting less pre-shared maximally entangled states. We show that a class of -ary EAQMDS have minimum distance upper limit greater than . Some of them have much larger minimum distance than the known quantum MDS (QMDS) codes of the same length. Most of these -ary EAQMDS codes are new in the sense that their parameters are not covered by the codes available in the literature.
Cite
@article{arxiv.1803.04168,
title = {Entanglement-assisted quantum MDS codes from constacyclic codes with large minimum distance},
author = {Liangdong Lu and Wenping Ma and Ruihu Li and Yuena Ma and Yang Liu and Hao Cao},
journal= {arXiv preprint arXiv:1803.04168},
year = {2018}
}