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Qldpc Advanced Quantum Codes

Quantum error-correcting codes from matrix-product codes related to quasi-orthogonal and quasi-unitary matrices

arXiv
Authors: Meng Cao

Year

2020

Paper ID

384

Status

Preprint

Abstract Read

~2 min

Abstract Words

110

Citations

N/A

Abstract

Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain self-orthogonality over finite fields is an effective way to obtain good q-ary quantum codes of large length. This article has two purposes: the first is to summarize some results of this topic obtained by the author of this article and his cooperators in [10-12]; the second is to add some new results on quasi-orthogonal matrices (resp. quasi-unitary matrices), Euclidean dual-containing (resp. Hermitian dual-containing) matrix-product codes and q-ary quantum codes derived from these matrix-product codes.

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  • This paper contributes to the qLDPC & Advanced Quantum Codes research area in the Quantum Articles archive.
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  • Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2012.15691 [2] arXiv https://arxiv.org/abs/2012.15691 [3] Publisher https://arxiv.org/abs/2012.15691

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