A class of twisted generalized Reed-Solomon codes

Zhang, Jun; Zhou, Zhengchun; Tang, Chunming

doi:10.48550/arxiv.2202.09011

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2022

2024

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“…Recently, the authors gave the parity check matrix for the TGRS code and obtained some self-dual TGRS codes with small Singleton defect [14], [27]. More relative results about self-orthogonal TGRS codes can be seen in [28], [29], [11].…”

Section: Introductionmentioning

confidence: 99%

The non-GRS properties for the twisted generalized Reed-Solomon code and its extended code

Zhu¹,

Liao²

2022

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In 2017, Beelen et al. firstly introduced twisted generalized Reed-Solomon (in short, TGRS) codes, and constructed a large subclass of MDS TGRS codes. Later, they proved that TGRS code is non-GRS when the code rate is less than one half. In this letter, basing on the dual code of the TGRS code or the extended TGRS code, by using the Schur product, we prove that almost all of TGRS codes and extended TGRS codes are non-GRS when the code rate more than one half.

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