The Hulls of Matrix-Product Codes over Commutative Rings and Applications

Abstract

Given a commutative ring $R$ with identity, a matrix $A\in M_{s\times l}(R)$, and $R$-linear codes ${\mathcal{C}}_1,\dots ,{\mathcal{C}}_s$ of the same length, this article considers the hull of the matrix-product codes $[{\mathcal{C}}_1\dots {\mathcal{C}}_s]A$. Consequently, it introduces various sufficient conditions under which $[{\mathcal{C}}_1\dots {\mathcal{C}}_s]A$ is a linear complementary dual (LCD) code. As an application, LCD matrix-product codes arising from torsion codes over finite chain rings are considered. Highlighting examples are also given.

10 pages