Two Families of Linear Codes Containing Non-GRS MDS Codes

Abstract: We construct two new families of linear codes by modifying the generator matrices of generalized Reed-Solomon (GRS) codes. For these codes, we explicitly derive parity-check matrices and establish necessary and sufficient conditions ensuring the MDS property. Additionally, we explore subfamilies within these constructions that are non-GRS MDS codes. We also characterize their self-orthogonal and self-dual properties and present some explicit constructions and examples.