Skew-cyclic codes

Delphine Boucher (1) , Willi Geiselmann (2) , Félix Ulmer (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 TH - Universität Karlsruhe

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.

Mots clés: linear codes; error connecting codes; BCH codes

Domaines: Anneaux et algèbres [math.RA]

Delphine Boucher, Willi Geiselmann, Félix Ulmer. Skew-cyclic codes. Applicable Algebra in Engineering, Communication and Computing, 2007, 18 (4), pp.379-389. ⟨10.1007/s00200-007-0043-z⟩. ⟨hal-00023483⟩