On self-orthogonality and self-duality of matrix-product codes over commutative rings

Self-orthogonal codes and self-dual codes, on the one hand, matrix-product other, form important sought-after classes of linear codes. Combining two constructions would be advantageous. Adding to this combination relaxation underlying algebraic structures commutative rings instead fields even more The current article paves a path in direction. authors study problem self-orthogonality self-duality over ring with identity. Some methods as well special matrices are introduced for construction such A characterization some cases is also given. concrete examples applications torsion presented.