Matrix-Product Constructions for Hermitian Self-Orthogonal Codes

Abstract

Self-orthogonal codes have been of interest due to there rich algebraic structures and wide applications. Euclidean self-orthogonal codes have been quite well studied in literature. Here, we have focused on Hermitian self-orthogonal codes. Constructions of such codes have been given based on the well-known matrix-product construction for linear codes. Criterion for the underlying matrix and the input codes required in such constructions have been determined. In many cases, the Hermitian self-orthogonality of the input codes and the assumption that the underlying matrix is unitary can be relaxed. Some special matrices used in the constructions and illustrative examples of good Hermitian self-orthogonal codes have been provided as well.