Modul: MAT076 Arbeitsgemeinschaft in Codierungstheorie und Kryptographie

## Non projective Frobenius algebras and linear codes

Prof. Dr. Francisco Javier Lobillo Borrero talk

Speaker invited by: Prof. Dr. Joachim Rosenthal

**Date:** 20.02.19 **Time:** 15.00 - 17.00 **Room:**

We extend the notion of a Frobenius algebra, dropping the projectivity condition, to grant that a Frobenius algebra over a Frobenius commutative ring is itself a Frobenius ring. The modification introduced here also allows Frobenius finite rings to be precisely those rings which are Frobenius finite algebras over their characteristic subrings. From the perspective of linear codes, our work expands one’s options to construct new finite Frobenius rings from old ones. We close with a discussion of generalized versions of the McWilliam identities that may be obtained in this context.