Recently some mixed alphabet rings are involved in constructing few-Lee weight codes with optimal or minimal Gray images using suitable defining sets or down-sets. Inspired by these works, we choose the mixed alphabet ring $\mathbb{Z}_2\mathbb{Z}_2[u]$ to construct a special class of linear code $C_L$ over $\mathbb{Z}_2[u]$ with $u^2=0$ by employing simplicial complexes generated by a single maximal element. We show that $C_L$ has few-Lee weights by determining the Lee weight distribution of $C_L$. Also we have an infinite family of minimal codes over $\mathbb{Z}_2$ via Gray map, which can be used to secret sharing schemes.

翻译：最近,一些混合字母环参与了使用合适的定义集或下层设置,用最优或最微小的灰色图像来构建几升重量代码。受这些作品的启发,我们选择混合字母环 $\mathbb ⁇ 2\mathb ⁇ 2[u] 美元,用美元2美元[u] =0美元构建一个特殊的线性代码类别 $C_L$, 超过$mathbb ⁇ 2[u]美元, 使用单一最大元素生成的简化复合体。我们通过确定李重量分布的$C_L$, 显示$C_L$少负重量。我们还有一个无限的最小代码家族,通过灰色地图超过$\mathbb ⁇ 2$, 可用于秘密共享计划。