English

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 qq-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 qq-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}
}