  Maximum distance separable (MDS) are constructed to required specifications.
The codes are explicitly given over finite fields with efficient encoding and
decoding algorithms. Series of such codes over finite fields with ratio of
distance to length approaching $(1-R)$ for given $R, \, 0 < R < 1$ are derived.
For given rate $R=\frac{r}{n}$, with $p$ not dividing $n$, series of codes over
finite fields of characteristic $p$ are constructed such that the ratio of the
distance to the length approaches $(1-R)$. For a given field $GF(q)$ MDS codes
of the form $(q-1,r)$ are constructed for any $r$.
  The codes are encompassing, easy to construct with efficient encoding and
decoding algorithms of complexity $\max\{O(n\log n), t^2\}$, where $t$ is the
error-correcting capability of the code.
