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

TL;DR

This paper introduces four novel methods for constructing self-orthogonal matrix-product codes using Toeplitz matrices, with applications in quantum code construction and efficient matrix generation.

Contribution

It presents new constructions of self-orthogonal matrix-product codes associated with Toeplitz matrices, including algorithms and applications in quantum coding.

Findings

Four new constructions of self-orthogonal matrix-product codes.

An efficient algorithm for generating Toeplitz-based matrices.

Applications in quantum code development.

Abstract

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.