Séminaire d'algèbre et de géométrie du 07-11-2022
Exposé de César Polcino Miliès
Le 07-11-2022 à 14:00, en P108.Essential idempotents in group algebras and codes
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Résumé
We shall review the motivation and definition of an essential idempotent and consider its characterizations. Then we will discuss some of the applications of this idea and, in particular, show that for minimal codes, there is no advantage in moving from cyclic groups to Abelian groups. We include an example to show that Abelian codes can be more convenient than cyclic ones when codes are not minimal. We also discuss the role of essential idempotents in describing simplex codes and codes of constant weight. Finally, we discuss the relations between essential idempotents of group algebras of a cyclic group of order n and of another cyclic group naturally associated with it.