Construction of linear codes over $\mathfrak{R}=\sum_{s=0}^{4} v_{5}^{s}\mathcal{A}_{4}$

Abstract

The aim of this paper is to propose a new family of codes. We define this family over the ring R=∑^4_{s=0}v^s_5A_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.