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Matrix-product codes over finite fields are an important class of long linearcodes by combining several commensurate shorter linear codes with a definingmatrix over finite fields. The construction of matrix-product codes withcertain self-orthogonality over finite fields is an effective way to obtaingood $q$-ary quantum codes of large length. This article has two purposes: thefirst is to summarize some results of this topic obtained by the author of thisarticle and his cooperators in [10-12]; the second is to add some new resultson quasi-orthogonal matrices (resp. quasi-unitary matrices), Euclideandual-containing (resp. Hermitian dual-containing) matrix-product codes and$q$-ary quantum codes derived from these matrix-product codes.

Quantum error-correcting codes from matrix-product codes related to quasi-orthogonal and quasi-unitary matrices