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

• URL: http://arxiv.org/abs/2012.15691v2
• Date: Sun, 30 Oct 2022 16:33:30 GMT
• Title: Quantum error-correcting codes from matrix-product codes related to quasi-orthogonal and quasi-unitary matrices
• Authors: Meng Cao
• Abstract summary: Matrix-product codes over finite fields are an important class of long linear codes. 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.
• Score: 18.763290930749235
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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