On a group under which symmetric Reed–Muller codes are invariant
Journal of Algebra and its Applications, vol.25, no.1, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 25 Issue: 1
- Publication Date: 2026
- Doi Number: 10.1142/s0219498825502950
- Journal Name: Journal of Algebra and its Applications
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
- Keywords: affine invariant, automorphism groups, Reed–Muller codes, symmetric Reed–Muller codes
- Open Archive Collection: AVESIS Open Access Collection
- Middle East Technical University Affiliated: Yes
Abstract
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.