Two Families of Linear Codes Containing Non-GRS MDS Codes

Kanat Abdukhalikov; Gyanendra K. Verma

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arXiv · 2512.13429

Two Families of Linear Codes Containing Non-GRS MDS Codes

Kanat Abdukhalikov·Gyanendra K. Verma

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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.

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Kanat Abdukhalikov, Gyanendra K. Verma. 2025-12-15. Two Families of Linear Codes Containing Non-GRS MDS Codes. https://arxiv.org/abs/2512.13429

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