  A large class of MDS linear codes is constructed. These codes are endowed
with an efficient decoding algorithm. Both the definition of the codes and the
design of their decoding algorithm only require from Linear Algebra methods,
making them fully accesible for everyone. Thus, the first part of the paper
develops a direct presentation of the codes by means of parity-check matrices,
and the decoding algorithm rests upon matrix and linear maps manipulations. The
somewhat more sophisticated mathematical context (non-commutative rings) needed
for the proof of the correctness of the decoding algorithm is postponed to the
second part. A final section locates the Reed-Solomon skew-differential codes
introduced here within the general context of codes defined by means of skew
polynomial rings.
