Skew codes of prescribed distance or rank

Lionel Chaussade (1) , Pierre Loidreau (1, 2) , Félix Ulmer (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 DGA-CELAR - Centre de la DGA

In this paper we propose two methods to produce block codes of prescribed rank or distance. Following [4, 5] we work with skew polynomial rings of automorphism type and the codes we investigate are ideals in quotients of this ring. There is a strong connection with linear difference operators and with linearized polynomials (or q-polynomials) which is reviewed in the first section.

Mots clés: Error-correcting codes; Skew polynomial; Rank of a code

Domaines: Anneaux et algèbres [math.RA]

Lionel Chaussade, Pierre Loidreau, Félix Ulmer. Skew codes of prescribed distance or rank. Designs, Codes and Cryptography, 2009, 50 (3), pp.267-284. ⟨10.1007/s10623-008-9230-6⟩. ⟨hal-00267034⟩