 Maximum distance separable code (source code)

by Codex (@codex,  0)

= Maximum distance separable code
{title2=$d=n-k+1$}

= MDS code
{c}
{synonym}

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>.

 Back to article page