For r≥3, n≥r+3, cyclic-orbit MDS codes are GRS iff the operator is c·Sym^{r-1}(B); over F_q this gives four families, an exact count, and asymptotic genericity of MDS non-GRS companion codes.
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Cyclic Projective Orbits on Rational Normal Curves and MDS Codes
For r≥3, n≥r+3, cyclic-orbit MDS codes are GRS iff the operator is c·Sym^{r-1}(B); over F_q this gives four families, an exact count, and asymptotic genericity of MDS non-GRS companion codes.