论对称里德-穆勒码不变的群组

arXiv - CS - Information Theory Pub Date : 2024-01-21 DOI:arxiv-2401.11496

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

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引用次数: 0

摘要

里德-穆勒码是编码理论中被广泛研究的纠错码系列。2020 年，Wei Yan 和 Sian-Jheng Lin 提出了 Reed-Muller 码的一种变体，称为对称 Reed-Muller 码。我们研究了对称里德-穆勒码自形群的线性映射，并证明这些线性映射的集合构成了一般线性群的一个子群，而一般线性群是穿刺里德-穆勒码的自形群。我们提供了一种方法，可以在某些特殊情况下明确确定这个子群中的所有自变群。

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

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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arXiv - CS - Information Theory

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