The equivalence of GRS codes and EGRS codes
Abstract
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 Fq be the q elements finite field, where q is the power of a prime. For a linear code C over Fq with length 2 n q, we prove that C is a GRS code if and only if C is a EGRS code.
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