Conference abstracts

Session S05 - Rings and Algebras

July 28, 16:10 ~ 16:35

## Essencial idempotents in group algebras and coding theory

### Universidade de São Paulo, Brazil   -   polcinomilies@gmail.com

We introduce the concept of essencial idempotents in group algebras, a notion inspired in coding theory. We shall give some criteria to identify which primitive idempotents are essential, and discuss some applications. Among these, we show that every minimal non-cyclic abelian code is a repetition code, and that every minimal abelian code is combinatorially equivalent to a cyclic code of the same lenth. Also, we shall give an example showing that a non minimal abelian code of lenth $p^2$ with $p$ a prime integer, can be more convenient than any cyclic code of that length.