Maximum distance separable code ($d=n-k+1$)

A nonzero length-$n$, dimension-$k$ linear code is maximum distance separable if its minimum Hamming distance equals $n-k+1$, attaining the Singleton bound. Reed-Solomon codes and generalized Reed-Solomon codes provide examples because a nonzero polynomial of degree at most $k-1$ has at most $k-1$ distinct polynomial roots.