Skew-Constacyclic Codes Over F_q [v]/ ‹ v^q -v ›

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Résumé

In this paper, we investigate the algebraic structure of the
non-chain ring F_q [v]/ ‹ v^q -v › , followed by the description of its
group automorphisms to get the algebraic structure of codes and their
dual over this ring. Further, we explore the algebraic structure of
skew-constacyclic codes by showing that their images by a linear Gray
map are skew-multi-twisted codes and determine their generator
polynomials. Finally, we characterize self-dual skew-constacyclic
codes over F_q [v]/ ‹ v^q -v › , and give conditions on the existence
of self-dual skew cyclic and self-dual skew negacyclic codes over F_q [v]/ ‹ v^q -v ›

Mots-clés

non-chain ring, skew-constacyclic codes, Gray map, self-dual skew codes