On $\sigma$ self-orthogonal matrix-product codes associated with Toeplitz matrices
<|reference_start|>On $\sigma$ self-orthogonal matrix-product codes associated with Toeplitz matrices: In this paper, we present four general constructions of $\sigma$ self-orthogonal matrix-product codes associated with Toeplitz matrices. The first one relies on the $\sigma'$ dual of a known $\sigma'$ dual-containing matrix-product code; the second one is founded on quasi-$\widehat{\sigma}$ matrices, where we provide an efficient algorithm for generating them on the basic of Toeplitz 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 in $\widetilde{\tau}$-optimal defining matrices.<|reference_end|>
@article{li2024on,
    title={On $\sigma$ self-orthogonal matrix-product codes associated with
  Toeplitz matrices},
    author={Yang Li, Shixin Zhu and Edgar Mart'inez-Moro},
    journal={arXiv preprint arXiv:2405.06292},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.06292},
    primaryClass={cs.IT math.IT}
}