On σ self-orthogonal matrix-product codes associated with Toeplitz matrices

In this paper, we present four general constructions of σ self-orthogonal matrix-product codes associated with Toeplitz matrices. The first one relies on the σ' dual of a known σ' dual-containing matrix-product code; the second one is founded on quasi-σ 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 τ-optimal defining matrices.