On the automorphisms of generalized algebraic geometry codes

ŞENEL E., ÖKE F.

Designs, Codes, and Cryptography, cilt.90, sa.6, ss.1369-1379, 2022 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 90 Sayı: 6
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s10623-022-01043-1
  • Dergi Adı: Designs, Codes, and Cryptography
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, PASCAL, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1369-1379
  • Anahtar Kelimeler: Algebraic function fields, Automorphism groups of function fields, Code automorphisms, Generalized algebraic geometry codes, Geometric Goppa codes
  • Trakya Üniversitesi Adresli: Evet

Özet

We consider the class of generalized algebraic geometry codes (GAG codes) formed by two collections of places, with places of the same degree in each collection. We introduce the concept of N1N2-automorphism group of a GAG code in this class-that is, a subgroup of the automorphism group of the code. Then we determine a subgroup of the N1N2-automorphism group in the general case and the N1N2-automorphism group itself in the rational function field case. We also explicitly construct such a group. This paper presents a method to obtain similar results for the GAG codes that have more collections of places of the same degree in their construction.