The equivalence of GRS codes and EGRS codes

04/25/2022

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by   Canze Zhu, et al.

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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 𝒞 over 𝔽_q with length 2≤ n≤ q, we prove that 𝒞 is a GRS code if and only if 𝒞 is a EGRS code.