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<p>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.</p>

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Two families of linear codes containing non-GRS MDS codes

  • 期刊论文

  • 发表日期：

    2026年6月18日

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  • Kanat Abdukhalikov,
  • Gyanendra K. Verma

摘要

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.