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Essential idempotents in group algebras and coding theory

Author

Listed:
  • Raul A. Ferraz

    (Universidade de São Paulo)

  • C. Polcino Milies

    (Universidade de São Paulo)

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.

Suggested Citation

  • Raul A. Ferraz & C. Polcino Milies, 2021. "Essential idempotents in group algebras and coding theory," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(3), pages 747-760, September.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:3:d:10.1007_s13226-021-00187-5
    DOI: 10.1007/s13226-021-00187-5
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