Essential idempotents in group algebras and coding theory

Raul A. Ferraz () and C. Polcino Milies ()
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Raul A. Ferraz: Universidade de São Paulo
C. Polcino Milies: Universidade de São Paulo

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 3, 747-760

Abstract: Abstract We consider a special class of idempotent of semisimple group algebras which we call essential. We give some criteria to decide when a primitive idempotent is essential; then we consider group algebras of cyclic group over finite fields, establish the number of essential idempotents in this case and find a relation among essential idempotents in different algebras. Finally we apply this ideas to coding theory and compute examples of codes with the best known weight.

Date: 2021
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DOI: 10.1007/s13226-021-00187-5

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