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The equivalence of GRS codes and EGRS codes

04/25/2022
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by   Canze Zhu, et al.
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NetEase, Inc
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Generalized Reed-Solomon and extended generalized Reed-Solomon (abbreviation to GRS and EGRS) codes are the most well-known family of MDS codes with wide applications in coding theory and practice. Let 𝔽_q be the q elements finite field, where q is the power of a prime. For a linear code ğ’ž over 𝔽_q with length 2≤ n≤ q, we prove that ğ’ž is a GRS code if and only if ğ’ž is a EGRS code.

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