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On a group under which symmetric Reed–Muller codes are invariant
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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
Journal
Journal of Algebra and its Applications
DOI
https://doi.org/10.1142/s0219498825502950
Collections
Graduate School of Applied Mathematics, Article
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S. K. Toplu, T. ARIKAN, P. AYDOĞDU, and O. Yayla, “On a group under which symmetric Reed–Muller codes are invariant,”
Journal of Algebra and its Applications
, pp. 0–0, 2024, Accessed: 00, 2024. [Online]. Available: https://hdl.handle.net/11511/110355.