A Gröbner basis approach to m-dimensional skew (consta-) cyclic codes
Résumé
Algebraic linear codes J/I ⊂ Fq[X1,. .. Xm]/I that are finite dimension quotients of multivariate polynomial rings, have been studied intensively; in particular m-dimensional cyclic codes where the ideal I is (X n 1 1 − 1,. .. , X nm m − 1). Recently this notion has been extended to two dimensional skew cyclic codes using multivariate skew polynomial rings over fields [12, 16, 18] and even over rings [15]. In this paper we use a Gröbner basis approach in order to generalize algebraic linear codes and m-dimensional cyclic codes to the skew polynomial rings setting. The approach encompass all previous results on m-dimensional (consta-)cyclic codes and allows for many generalizations.
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