Quantum error-correcting codes from matrix-product codes related to quasi-orthogonal and quasi-unitary matrices
Information Theory
2022-11-01 v2 math.IT
Quantum Physics
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 -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 -ary quantum codes derived from these matrix-product codes.
Keywords
Cite
@article{arxiv.2012.15691,
title = {Quantum error-correcting codes from matrix-product codes related to quasi-orthogonal and quasi-unitary matrices},
author = {Meng Cao},
journal= {arXiv preprint arXiv:2012.15691},
year = {2022}
}