Séminaire d'algèbre et de géométrie du 03-12-2025

Exposé de Nabil Bennenni

Le 03-12-2025 à 15:00, en P108 et en ligne.

Mixed skew cyclic codes

Résumé

We investigate various families of skew cyclic codes by constructing specialized subclasses that exhibit enhanced and desirable algebraic properties. Our focus is on skew cyclic codes de ned over mixed rings, particularly the mixed alphabet ring (Fq(Fq + vFq)) equipped with a mixed automorphism ((theta, theta~)). We analyze their algebraic and structural behavior and describe their characterization for arbitrary lengths via the associated non-commutative ring (Fq [x,theta] (Fq +vFq) [x,theta~]). Furthermore, we establish conditions ensuring the existence of linear complementary dual (LCD) skew cyclic codes, which are particularly relevant due to their applications in enhancing resistance against side-channel and fault-injection attacks.