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Trace Codes with Few Weights over $\mathbb{F}_p+u\mathbb{F}_p$ (1612.00128v1)
Published 1 Dec 2016 in cs.IT and math.IT
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.