Construction of linear codes over $\mathfrak{R}=\sum_{s=0}^{4} v_{5}^{s}\mathcal{A}_{4}$
The aim of this paper is to propose a new family of codes. We define this family over the ring $\mathfrak{R}=\sum_{s=0}^{4} v_{5}^{s}\mathcal{A}_{4}$, with $v_{5}^{5}=v_{5}$. We derive its properties, a generator matrix and Gray images. This new family of codes is illustrated by three applications.