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arXiv · 1612.01096

Linear Codes over $\mathbb{F}_{q}[x]/(x^2)$ and $GR(p^2,m)$ Reaching the Griesmer Bound

Jin Li·Aixian Zhang·Keqin Feng
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Abstract

We construct two series of linear codes over finite ring $\mathbb{F}_{q}[x]/(x^2)$ and Galois ring $GR(p^2,m)$ respectively reaching the Griesmer bound. They derive two series of codes over finite field $\mathbb{F}_{q}$ by Gray map. The first series of codes over $\mathbb{F}_{q}$ derived from $\mathbb{F}_{q}[x]/(x^2)$ are linear and also reach the Griesmer bound in some cases. Many of linear codes over finite field we constructed have two Hamming (non-zero) weights.

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Jin Li, Aixian Zhang, Keqin Feng. 2016-12-04. Linear Codes over $\mathbb{F}_{q}[x]/(x^2)$ and $GR(p^2,m)$ Reaching the Griesmer Bound. https://arxiv.org/abs/1612.01096

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