季制芦苇-穆勒码及其最小权基

2021 XVII International Symposium "Problems of Redundancy in Information and Control Systems" (REDUNDANCY) Pub Date : 2021-10-25 DOI:10.1109/REDUNDANCY52534.2021.9606466

F. Solov'eva

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引用次数: 0

摘要

证明了2009年BQ-Plotkin构造得到的四元Reed - Muller码族具有最小权码字基。在2020年，我们发现用四元Plotkin方法构造的四元Reed - Muller码具有最小的权基。结合这两种结构，我们证明了所有已知的四元线性Reed - Muller码都有最小权码字基。基是迭代得到的。

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Quaternary Reed – Muller codes and their minimum weight bases

We prove that the families of quaternary Reed – Muller codes obtained by the BQ-Plotkin construction 2009 have bases of minimum weight codewords. In 2020 we found that the quaternary Reed – Muller codes constructed by the quaternary Plotkin approach have the minimum weight bases. Combining these two constructions we prove that all known quaternary linear Reed – Muller codes have bases of minimum weight codewords. The bases are obtained iteratively.

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2021 XVII International Symposium "Problems of Redundancy in Information and Control Systems" (REDUNDANCY)

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