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

TL;DR

This paper investigates the properties of self-orthogonality and self-duality in matrix-product codes over commutative rings, introducing new methods and characterizations for constructing such codes with concrete examples.

Contribution

It introduces new methods and characterizations for constructing self-orthogonal and self-dual matrix-product codes over commutative rings.

Findings

Methods for constructing self-orthogonal and self-dual MPCs

Characterization of MPCs in a special case

Concrete examples illustrating the concepts

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.