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arXiv · 1609.09531

The Generalized Reed-Muller codes in a modular group algebra

Harinaivo Andriatahiny·Vololona Harinoro Rakotomalala
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Abstract

First we study some properties of the modular group algebra $\mathbb{F}_{p^r}[G]$ where $G$ is the additive group of a Galois ring of characteristic $p^r$ and $\mathbb{F}_{p^r}$ is the field of $p^r$ elements. Secondly a description of the Generalized Reed-Muller codes over $\mathbb{F}_{p^r}$ in $\mathbb{F}_{p^r}[G]$ is presented.

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Harinaivo Andriatahiny, Vololona Harinoro Rakotomalala. 2016-09-29. The Generalized Reed-Muller codes in a modular group algebra. https://arxiv.org/abs/1609.09531

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