Trace Codes with Few Weights over $\mathbb{F}_p+u\mathbb{F}_p$
Information Theory
2017-01-05 v1 math.IT
Abstract
We construct an infinite family of two-Lee-weight and three-Lee-weight codes over the chain ring 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 . 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.
Keywords
Cite
@article{arxiv.1612.00128,
title = {Trace Codes with Few Weights over $\mathbb{F}_p+u\mathbb{F}_p$},
author = {Minjia Shi and Yan Liu and Patrick Solé},
journal= {arXiv preprint arXiv:1612.00128},
year = {2017}
}
Comments
12 pages, submitted on 27 October, 2016. arXiv admin note: text overlap with arXiv:1612.00126, arXiv:1612.00118