Essential idempotents in group algebras and coding theory
type: Item
instance of: scholarly article
title: Essential idempotents in group algebras and coding theory
author: Raul Antonio Ferraz
author: C. Polcino Milies
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2022-01-07T00:00:00Z
review text: 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.
reviewed by: Carolin Hannusch
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 94B60
zbMATH DE Number: 7453738
zbMATH Keywords: essential idempotents
zbMATH Keywords: idempotent elements
describes a project that uses: Code Tables
MaRDI profile type: Publication
full work available at URL: s13226-021-00187-5
OpenAlex ID: W3215827034
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DOI: 10.1007/S13226-021-00187-5
description: scientific article; zbMATH DE number 7453738