Séminaire d'algèbre et de géométrie du 23-01-2025

Exposé de Ramy Farouk Hussein Taki El-din

Le 23-01-2025 à 14:00, en P108 et en ligne.

Multi-twisted codes as a generalization of cyclic codes

Résumé

We begin with the algebraic structure of cyclic codes over finite fields. This structure is subjected to a series of generalizations to provide algebraic descriptions of constacyclic, quasi-cyclic, quasi-twisted, generalized quasi-cyclic, and multi-twisted (MT) codes. The correspondences between MT codes and submodules of (F_q[x])^l are illustrated. Hence, an MT code has a basis, which is used to construct a generator matrix with polynomial entries, called the generator polynomial matrix (GPM). Several properties of the GPM are shown.