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

Date

2024-1-01

Author

Toplu, Sibel Kurt
ARIKAN, TALHA
AYDOĞDU, PINAR
Yayla, Oğuz

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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.

Subject Keywords

affine invariant, automorphism groups, Reed–Muller codes, symmetric Reed–Muller codes

URI

https://hdl.handle.net/11511/110355

Collections

Graduate School of Applied Mathematics, Article