伽罗瓦环上兰克度量编码的麦克威廉斯等式

arXiv - MATH - Information Theory Pub Date : 2024-08-06 DOI:arxiv-2408.03237

Iván Blanco-Chacón, Alberto F. Boix, Marcus Grefferath, Erik Hieta-aho

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引用次数: 0

摘要

本文旨在研究伽罗瓦环上的秩度量编码。特别是，我们证明了有限链环的麦克威廉斯同一性（MacWilliams identity），它与代码及其对偶的 $q$ 二项式矩的序列有关；对于伽罗瓦环上的自由代码的伽比杜利南类似码，我们证明了相应的麦克威廉斯同一性，它是一个函数表达式，与对偶的权重枚举器和原代码权重枚举器的麦克威廉斯变换以及附加在零除数上的一个额外项有关。

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MacWilliams Identities for Rank metric codes over Galois rings

The purpose of this paper is to study rank metric codes over Galois rings. In particular, we prove MacWilliams identities for finite chain rings relating the sequences of $q$-binomial moments of a code and its dual and for Gabidulin analogues of free codes over Galois rings we prove the corresponding MacWilliams identity as a functional expression relating the weight enumerator of the dual with the MacWilliams transform of the weight enumerator of the original code plus one extra term attached to the zero divisors.

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arXiv - MATH - Information Theory

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