On a Group Under Which Symmetric Reed-Muller Codes are Invariant

Sibel Kurt Toplu; Talha Arikan; Pinar AydoğDu; OğUz Yayla

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arXiv · 2401.11496

On a Group Under Which Symmetric Reed-Muller Codes are Invariant

Sibel Kurt Toplu·Talha Arikan·Pinar AydoğDu·OğUz Yayla

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Abstract

The Reed-Muller codes are a family of error-correcting codes that have been widely studied in coding theory. In 2020, Wei Yan and Sian-Jheng Lin introduced a variant of Reed-Muller codes so 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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Sibel Kurt Toplu, Talha Arikan, Pinar AydoğDu, OğUz Yayla. 2024-01-21. On a Group Under Which Symmetric Reed-Muller Codes are Invariant. https://arxiv.org/abs/2401.11496

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