  We generalize the notion of cyclic codes by using generator polynomials in
(non commutative) skew polynomial rings. Since skew polynomial rings are left
and right euclidean, the obtained codes share most properties of cyclic codes.
Since there are much more skew-cyclic codes, this new class of codes allows to
systematically search for codes with good properties. We give many examples of
codes which improve the previously best known linear codes.
