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<p>MDS codes are widely applied in communication systems due to their good error-correcting abilities. Constructing non-GRS type MDS codes is an interesting topic in the coding theory. In this paper, we have constructed a novel extended code from the extended twisted generalized Reed-Solomon code. We provide the necessary and sufficient conditions for our codes being MDS and NMDS. Additionally, we not only prove that the MDS codes from our codes are inequivalent to the GRS codes, but also show that the NMDS codes from our codes are inequivalent to the Roth-Lempel codes.</p>

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MDS and NMDS codes from extended codes of extended twisted Reed-Solomon codes

  • 期刊论文

  • 发表日期：

    2026年2月17日

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  • Jiayu Ma,
  • Jiahui Wang,
  • Yang Ding

摘要

MDS codes are widely applied in communication systems due to their good error-correcting abilities. Constructing non-GRS type MDS codes is an interesting topic in the coding theory. In this paper, we have constructed a novel extended code from the extended twisted generalized Reed-Solomon code. We provide the necessary and sufficient conditions for our codes being MDS and NMDS. Additionally, we not only prove that the MDS codes from our codes are inequivalent to the GRS codes, but also show that the NMDS codes from our codes are inequivalent to the Roth-Lempel codes.