Minimal abelian codes of length p^n and 2p^n

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Kangal N., Köroğlu M. E.

7th International Conference on Mathematics “An Istanbul Meeting for World Mathematicians”, İstanbul, Türkiye, 11 Temmuz - 13 Eylül 2023, ss.181

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.181
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

Let F_q  be a finite field with q elements and G be a finite abelian group such that (Q , |G| )=1. Then the group algebra F_qG is semisimple and its ideals can be expressed by means of the primitive idempotents of F_qG. Minimal codes can be considered as the minimal ideals of the group algebra F_qG and minimal ideals can be represented by primitive idempotents. In this talk, we will give a survey of tne literature on the known minimal codes of length p^n and 2p^n over finite abelian group algebras and their parameters.