Published January 1, 2024
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On a group under which symmetric Reed-Muller codes are invariant
- 1. Hacettepe Univ, Grad Sch Sci & Engn, TR-06800 Ankara, Turkiye
- 2. Hacettepe Univ, Dept Math, TR-06800 Ankara, Turkiye
- 3. Middle East Tech Univ, Inst Appl Math, TR-06800 Ankara, Turkiye
Description
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.
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