On general self-orthogonal matrix-product codes associated with Toeplitz matrices
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909402042204160 |
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| author | Li, Yang Zhu, Shixin Martínez-Moro, Edgar |
| author_facet | Li, Yang Zhu, Shixin Martínez-Moro, Edgar |
| contents | In this paper, we present four constructions of {general} self-orthogonal matrix-product codes associated with Toeplitz matrices. The first one relies on the {dual} of a known {general} dual-containing matrix-product code; the second one is founded on {a specific family of} matrices, where we provide an efficient algorithm for generating them {on the basis of Toeplitz matrices} and {it has an interesting application in producing new non-singular by columns quasi-unitary matrices}; and the last two ones are based on the utilization of certain special Toeplitz matrices. Concrete examples and detailed comparisons are provided. As a byproduct, we also find an application of Toeplitz matrices, which is closely related to the constructions of quantum codes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_06292 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On general self-orthogonal matrix-product codes associated with Toeplitz matrices Li, Yang Zhu, Shixin Martínez-Moro, Edgar Information Theory 94B05 15B05 12E10 In this paper, we present four constructions of {general} self-orthogonal matrix-product codes associated with Toeplitz matrices. The first one relies on the {dual} of a known {general} dual-containing matrix-product code; the second one is founded on {a specific family of} matrices, where we provide an efficient algorithm for generating them {on the basis of Toeplitz matrices} and {it has an interesting application in producing new non-singular by columns quasi-unitary matrices}; and the last two ones are based on the utilization of certain special Toeplitz matrices. Concrete examples and detailed comparisons are provided. As a byproduct, we also find an application of Toeplitz matrices, which is closely related to the constructions of quantum codes. |
| title | On general self-orthogonal matrix-product codes associated with Toeplitz matrices |
| topic | Information Theory 94B05 15B05 12E10 |
| url | https://arxiv.org/abs/2405.06292 |