On Self-Orthogonality and Self-Duality of Matrix-Product Codes over Commutative Rings

Abstract: Let $R$ be a commutative ring with identity. The paper studies the problem of self-orthogonality and self-duality matrix-product codes (MPCs) over $R$. Some methods as well as special matrices are introduced for the construction of such MPCs. A characterization of such codes (in a special case) is also given. Some concrete examples are presented throughout the paper.