Gray maps on linear codes over $\bm{\mathbb{F}_p[v]/(v^m-v)}$ and their\\ applications

In this paper, we define the general Gray maps on linear codes over $\mathbb{F}_p[v]/(v^m-v)$, which lead to Gray weights and Gray distances of linear codes. We give a special class of Gray maps, which preserve the property of self-dual of linear codes from the ring $\mathbb{F}_p[v]/(v^m-v)$ to the finite field $\mathbb{F}_p$. Moreover, a self-dual code $[16,8,6]$ with new weight distribution over $\mathbb{F}_7$ is obtained by a special Gray map.