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arXiv · 1612.00123

Optimal three-weight cubic codes

Minjia Shi·Hongwei Zhu·Patrick Solé
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Abstract

In this paper, we construct an infinite family of three-weight binary codes from linear codes over the ring $R=\mathbb{F}_2+v\mathbb{F}_2+v^2\mathbb{F}_2$, where $v^3=1.$ These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distributions are computed by employing character sums. The three-weight binary linear codes which we construct are shown to be optimal when $m$ is odd and $m>1$. They are cubic, that is to say quasi-cyclic of co-index three. An application to secret sharing schemes is given.

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Minjia Shi, Hongwei Zhu, Patrick Solé. 2016-12-01. Optimal three-weight cubic codes. https://arxiv.org/abs/1612.00123

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