Essential idempotents in group algebras and coding theory
In this paper, the authors investigate a class of semisimple group algebras. These group algebras also contain codes as ideals. Every ideal can be generated by an idempotent element. Therefore the authors introduce the definition of essential idempotent elements, which were called non-degenerate idempotents in the special case of group algebras of cyclic groups over finite fields previously. In Section 3, essential idempotents are investigated by the authors and previous results are mentioned before the authors prove their main results in Theorem 4 and Theorem 5. In Theorem 6, the number of essential idempotents in \(\mathbb{F}C_n,\) where \(\mathbb{F}\) denotes a finite field and \(C_n\) a cyclic group of order \(n.\) In Section 4, the authors investigate essential binary codes. In the end of the paper, the authors show some examples of essential codes. Additionally, they provide a program in GAP for the construction of idempotent elements.
scientific article; zbMATH DE number 7453738
scientific article