Trace Codes with Few Weights over $\mathbb{F}_p+u\mathbb{F}_p$

Minjia Shi; Yan Liu; Patrick Solé

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arXiv · 1612.00128

Trace Codes with Few Weights over $\mathbb{F}_p+u\mathbb{F}_p$

Minjia Shi·Yan Liu·Patrick Solé

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Abstract

We construct an infinite family of two-Lee-weight and three-Lee-weight codes over the chain ring $\mathbb{F}_p+u\mathbb{F}_p.$ They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using Gauss sums. Then by using a linear Gray map, we obtain an infinite family of abelian codes with few weights over $\mathbb{F}_p$. In particular, we obtain an infinite family of two-weight codes which meets the Griesmer bound with equality. Finally, an application to secret sharing schemes is given.

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Minjia Shi, Yan Liu, Patrick Solé. 2016-12-01. Trace Codes with Few Weights over $\mathbb{F}_p+u\mathbb{F}_p$. https://arxiv.org/abs/1612.00128

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