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Essential idempotents in group algebras and coding theory

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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.

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66.281, São Paulo, CEP 05314-970, Brazil

    Raul A. Ferraz & C. Polcino Milies

Authors
  1. Raul A. Ferraz
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  2. C. Polcino Milies
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Correspondence to Raul A. Ferraz.

Additional information

Communicated by Gadadhar Misra.

Dedicated to Prof. I.B.S. Passi on the occasion of his 80th birthday.

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Ferraz, R.A., Milies, C.P. Essential idempotents in group algebras and coding theory. Indian J Pure Appl Math 52, 747–760 (2021). https://doi.org/10.1007/s13226-021-00187-5

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  • DOI: https://doi.org/10.1007/s13226-021-00187-5

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