On a group under which symmetric Reed–Muller codes are invariant

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Toplu S. K., ARIKAN T., AYDOĞDU P., YAYLA O.

Journal of Algebra and its Applications, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1142/s0219498825502950
  • Dergi Adı: Journal of Algebra and its Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: affine invariant, automorphism groups, Reed–Muller codes, symmetric Reed–Muller codes
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

The Reed–Muller codes are a family of error-correcting codes that have been widely studied in coding theory. In 2020, Yan and Lin introduced a variant of Reed–Muller codes called symmetric Reed–Muller codes. We investigate linear maps of the automorphism group of symmetric Reed–Muller codes and show that the set of these linear maps forms a subgroup of the general linear group, which is the automorphism group of punctured Reed–Muller codes. We provide a method to determine all the automorphisms in this subgroup explicitly for some special cases.