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

This paper presents 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 based on 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, closely related to the constructions of quantum codes.